The Astronomical Journal, 147:94 (25pp), 2014 May doi:10.1088/0004-6256/147/5/94 C 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

THE SOLAR NEIGHBORHOOD. XXXII. THE HYDROGEN BURNING LIMIT∗,†

Sergio B. Dieterich1,4, Todd J. Henry1,4, Wei-Chun Jao1,4, Jennifer G. Winters1,4, Altonio D. Hosey1,4, Adric R. Riedel2,4, and John P. Subasavage3,4 1 Georgia State University, Atlanta, GA 30302-4106, USA; [email protected] 2 American Museum of Natural History, New York, NY 10024, USA 3 United States Naval Observatory, Flagstaff, AZ 86001, USA Received 2013 August 15; accepted 2013 November 30; published 2014 March 24

ABSTRACT We construct a Hertzsprung–Russell diagram for the stellar/substellar boundary based on a sample of 63 objects ranging in spectral type from M6V to L4. We report newly observed VRI photometry for all 63 objects and new trigonometric parallaxes for 37 objects. The remaining 26 objects have trigonometric parallaxes from the literature. We combine our optical photometry and trigonometric parallaxes with 2MASS and WISE photometry and employ a novel spectral energy distribution fitting algorithm to determine effective temperatures, bolometric , and radii. Our uncertainties range from ∼20 K to ∼150 K in temperature, ∼0.01 to ∼0.06 in log(L/L) and ∼3% to ∼10% in radius. We check our methodology by comparing our calculated radii to radii directly measured via long baseline optical interferometry. We find evidence for the local minimum in the radius–temperature and radius– trends that signals the end of the stellar and the start of the brown dwarf sequence at Teff ∼ 2075 K, log(L/L) ∼−3.9, and (R/R) ∼ 0.086. The existence of this local minimum is predicted by evolutionary models, but at temperatures ∼400 K cooler. The minimum radius happens near the locus of 2MASS J0523−1403, an L2.5 dwarf with V − K = 9.42. We make qualitative arguments as to why the effects of the recent revision in solar abundances accounts for the discrepancy between our findings and the evolutionary models. We also report new color–absolute magnitude relations for optical and infrared colors which are useful for estimating photometric distances. We study the optical variability of all 63 targets and find an overall variability +9 fraction of 36−7%atathresholdof15mmagintheI band, which is in agreement with previous studies. Key words: brown dwarfs – Hertzsprung–Russell and C–M diagrams – parallaxes – solar neighborhood – : fundamental parameters – stars: low-mass Online-only material: color figures, extended figures, machine-readable and VO tables

1. INTRODUCTION fails us when we most need it. While evolutionary models predict the minimal to be anywhere from 0.070 M The first comprehensive stellar structure and evolution models to 0.077 M (see Section 7.2), the lithium test only works for the low-mass end of the main sequence were published in the for masses 0.060 M due to the lower mass at which core late 20th century (e.g., Burrows et al. 1993; Baraffe et al. 1995). temperatures are sufficient to fuse lithium. While the predictions of these models are widely accepted The models for low-mass stars and brown dwarfs in current today, they remain largely unconstrained by observations. The usage (Burrows et al. 1993, 1997; Baraffe et al. 1998, 2003; problem is particularly noteworthy when it comes to the issue of Chabrier et al. 2000; Saumon & Marley 2008) predict the end distinguishing stellar objects from the substellar brown dwarfs. of the stellar main sequence at temperatures ranging from 1550 While the internal physics of stars and brown dwarfs is different, to 1750 K, corresponding roughly to spectral type L4. These their atmospheric properties overlap in the late M and early L models have achieved varying degrees of success, but as we spectral types, thus making them difficult to distinguish based discuss in Section 7.2, they are mutually inconsistent when it on photometric and spectroscopic features alone. One test used comes to determining the properties of the smallest possible to identify substellar objects—the lithium test (Rebolo et al. . The inconsistency is not surprising given that none of 1992)—relies on the fact that lithium undergoes nuclear burning these decade-old evolutionary models incorporates the state- at temperatures slightly lower than hydrogen and, therefore, of-the-art in atmospheric models, nor do they account for the should be totally consumed in fully convective hydrogen burning recent 22% downward revision in solar abundances (Caffau et al. objects at time scales  than their evolutionary time scales. 2011), which are in agreement with the results of solar astero- Detection of the Li λ6708 line would therefore signal the seismology.5 substellar nature of an object. This is a powerful test, but it Over the last 10 yr few changes were made to models for very low mass (VLM) stars and brown dwarfs in large part because the models provide predictions that are not directly ∗ Based in part on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project of the Ministerio´ da observable. Whereas an atmospheric model can be fully tested Ciencia,ˆ Tecnologia, e Inova¸cao˜ (MCTI) da Republica´ Federativa do Brasil, against an observed spectrum, testing an evolutionary model the U.S. National Optical Astronomy Observatory (NOAO), the University of requires accurate knowledge of mass, age, and as North Carolina at Chapel Hill (UNC), and Michigan State University (MSU). well as an accurate atmospheric model that serves as a boundary † Based in part on observations obtained via the Cerro Tololo Inter-American Observatory Parallax Investigation (CTIOPI), at the Cerro Tololo 0.9 m condition. telescope. CTIOPI began under the auspices of the NOAO Surveys Program in 1999, and continues via the SMARTS Consortium. 5 A review of the history of revisions to solar abundances, including issues 4 Visiting astronomer, Cerro Tololo Inter-American Observatory. related to solar asteroseismology, is given in Allard et al. (2013).

1 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. The problem of understanding the stellar/substellar boundary can essentially be formulated by posing two questions. The first one is: “What do objects close to either side of the stellar/substellar boundary look like to an observer?” The second question is: “What are the masses and other structural parameters of objects on either side of the stellar/substellar boundary?” While it is the second question that usually gets the most attention, we note that any attempt to determine masses at the stellar/substellar boundary assumes an inherently model dependent (and therefore possibly flawed) answer to the first question. What is needed is an observational test that relies as little on evolutionary models as possible. Because brown dwarfs are supported by electron degeneracy pressure, their internal physics is fundamentally different from that of stars. One manifestation of this difference is the reversal of the mass–radius relation at the hydrogen burning limit (Chabrier Figure 1. Spectral type distribution for the observed sample. M dwarfs are more et al. 2009; Burrows et al. 2011). Whereas, for stars, radius heavily sampled because most M dwarfs already had trigonometric parallaxes increases as a function of mass, the opposite is true for brown at the beginning of the study. Several L dwarf parallaxes are still in progress. dwarfs. The result is a pronounced minimum in radius at the hydrogen burning limit (see Section 7). ages >1 Gyr, we avoided objects with known youth signatures. To reveal the end of the stellar main sequence by identifying All targets have original distance estimates within 25 pc and are ◦ the minimum in the radius trend, we construct a bona fide located south of +30 . This declination requirement Hertzsprung–Russell (HR) diagram for the stellar/substellar makes all targets observable from CTIO. Of these 82 targets, boundary based on wide photometric coverage from ∼0.4 μm 26 have previously established trigonometric parallaxes. The to ∼17 μm, trigonometric parallaxes, and the new BT-Settl remaining 56 were placed on our parallax observing list. In this model atmospheres (Allard et al. 2012, 2013), which have paper, we report new trigonometric parallaxes for 37 targets and been shown to be highly accurate for M and L dwarfs (see new VRI photometry for all 63 targets that either have trigono- Section 5). We also employ a new custom-made iterative metric parallaxes from the literature or have new trigonometric spectral energy distribution (SED) fitting code that interpolates parallaxes reported here. Parallax observations for 19 targets between model grid points to determine effective temperatures are still ongoing and will be described in a future publication. and performs small adjustments to the SED templates based Figure 1 is a histogram showing the spectral type distribution on observed photometry to better determine luminosities. The of the observed sample for this paper. There are more M dwarfs results of our calculations are effective temperatures (Teff), than L dwarfs in Figure 1 because more M dwarfs had trigono- luminosities (log(L/L)), and radii (R/R), which we then use metric parallaxes from the literature. Once parallax observa- to construct the HR diagram as well as temperature–radius and tions for the 19 ongoing targets are finished the spectral type luminosity–radius diagrams. The latter two diagrams provide distribution will become nearly even. the same essential information as the HR diagram but facilitate the inspection of radius trends. 3. PHOTOMETRIC OBSERVATIONS The paper is organized as follows. We include all of our VLM stars and brown dwarfs have traditionally been studied observed and derived quantities in Table 1. The data presented in in the near infrared where they emit most of their flux. However, this table form the basis for subsequent discussions in the paper. as discussed in detail in Section 5, optical photometry is essential We discuss our observed sample in Section 2 and discuss the for determining the effective temperatures and the bolometric methodology of our photometric and astrometric observations fluxes of these very red objects. We obtained VRI photometry for in Sections 3 and 4, respectively. We discuss our SED fitting all targets in our sample using the CTIO 0.9 m telescope for the algorithms and check their results against radii measured with brighter targets and the SOAR Optical Imager camera on the long baseline optical interferometry in Section 5. We discuss SOAR 4.1m telescope for fainter targets. SOAR observations our new optical photometric results, trigonometric parallaxes, were conducted between 2009 September and 2010 December effective temperatures, color–magnitude relations, and optical during six observing runs comprising NOAO programs 2009B- variability in Sections 6.1–6.5. We discuss the newly discovered 0425, 2010A-0185, and 2010B-0176. A total of 17 nights on astrometric binary DENIS J1454−6604AB in Section 6.6.In SOAR were used for optical photometry. Column 16 of Table 1 Section 7, we discuss the end of the stellar main sequence based indicates which telescope was used for each target. The division on radius trends. We discuss individual objects in Section 8 and between the 0.9 m telescope and SOAR fell roughly along the make concluding remarks and discuss future work in Section 9. M/L divide. To ensure consistency, 28 targets were observed on 2. THE OBSERVED SAMPLE both telescopes. Essentially the same observing procedure was used for both Table 1 lists our observed sample. The goal of our target se- photometry programs. After determining that a night was likely lection was to obtain an observing list that samples the color to be entirely cloudless in the late afternoon, three or four continuum between spectral types M6V to L4, corresponding photometric standard fields were chosen and an observing to V−K ranging from 6.2 to 11.8, for the nearby Galactic disk schedule was constructed so that each field was observed at three population. Targets with known spectral types were selected different air masses, typically around 2.0, 1.5, and the lowest from the literature, with at least eight targets in each spectral possible air mass given the standard field’s declination. We used subclass, for a total of 82 targets. Because the differences be- the photometric standards compiled by Arlo Landolt (Landolt tween stellar and substellar objects become more pronounced at 1992, 2007, 2009) as well as standards from Bessel (1990)

2 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. d ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· .005 d,e,f .006 .008 d,e .008 d,e .004 .008 .008 .009 .005.003 d .005 .004 .005.003 f .004 .003 d .002 .005 d,f .007 .007 .005 .004 .004 .006 .003 .003 d .004 .003 .008 .002 .003 .004 .004 .006 .008 .005 .003 .009 )  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± R )( .048 0.105 .025 0.098 .046 0.110 .046 0.152 .011 0.109 .078 0.091 .076 0.093 .042 0.129 .029 0.104 .024 0.103 .015 0.098 .039 0.088 .009 0.122 .013 0.094 .021 0.089 .011 0.088 .019 0.102 .028 0.133 .057 0.108 .042 0.109 .030 0.133 .013 0.127 .017 0.110 .010 0.101 .012 0.157 .021 0.086 .022 0.128 .013 0.139 .017 0.113 .010 0.107 .016 0.132 .025 0.107 .016 0.129 .049 0.119 .056 0.119 .032 0.135 .018 0.125 .044 0.138  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± L/L 4.049 4.035 3.506 2.818 3.950 3.599 3.507 3.441 3.676 4.010 3.600 3.625 3.413 3.732 3.696 3.845 3.997 3.291 3.454 3.505 3.194 3.137 3.366 3.579 3.033 3.898 3.107 3.039 3.798 3.516 3.084 3.399 3.166 3.169 3.218 3.113 3.194 3.036 Luminosity Radius Notes − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − 21 49 57 21 33 34 29 19 37 40 71 57 25 41 19 27 56 31 51 32 47 37 27 30 66 27 24 36 32 13 13 27 25 22 28 38 54 56 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± eff ··· ··· ··· T VRI c Tel. .012 S 2 1725 .005 S 2 1797 .001.005 S S 2.022 2.026 S 2305 .012 S 2918 1 C.015 1.003 S 1796 3 C.009 2402 2 C.011 2513 3 C.017 2512 2 C.017 2656 3.030 S 2502 2 C.024 2312 2.032 S 2.012 S 2212 1 C.016 2532 1.032 S 2146 2.038 S 1783 2.005 S 2074 1.025 S 2313 1.026 S 2403 2.018 S 2310 1 C.006 2186 1 C.024 2295 2 C.029 2117 2 C.010 2690 2 C.036 2683 3 C.025 1922 3 C.025 2324 1 C 2680 3.027 2481 2.017 S 2588 C.040 2691 2 S 2.005 1804 1 C.031 2619 C.038 2376 2 S 2 2611 1 2595 2398 .025 S 1 2315 .014 C 2 2700 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± .045 16.76 .020 17.51 .010 16.69 .005 13.84 .016 15.92 .017 16.57 .008 13.88 .015 15.27 .004 10.65 .023 14.49 .007 14.01 .020 13.80 .025 16.79 .029 13.08 .015 16.84 .026 17.32 .021 16.52 .005 15.85 .023 16.19 .037 14.90 .020 16.39 .016 17.05 .025 16.01 .005 10.58 .017 13.44 .028 16.86 .015 14.44 .020 11.84 .035 15.20 .002 11.25 .033 14.91 .028 9.44 .045 17.66 .017 14.87 .048 14.84 .035 13.77 .030 13.50 .036 15.54 .016 15.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± .025 19.24 .010 20.11 .085 19.08 .045 15.67 .024 18.32 .051 19.14 .021 16.30 .050 17.70 .006 13.03 .002 16.98 .026 16.39 .053 16.08 .050 19.18 .005 15.49 .052 19.38 .037 19.77 .112 18.71 .050 18.38 .035 18.74 .038 17.42 .045 18.86 .053 19.45 .023 18.41 .033 12.88 .042 15.72 .068 19.16 .032 16.74 .032 14.12 .152 17.66 .057 13.63 .033 17.13 .008 11.64 .005 20.01 .049 17.27 .036 17.33 .009 16.02 .027 15.97 .039 17.99 .051 17.45 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± VR I ) Epochs (K) log( 1 − 8.4 20.01 tan 30.132.2 21.61 17.28 37.611.3 21.43 85.5 21.54 21.0 18.53 92.2 19.97 42.7 15.14 12.4 19.38 36.6 18.70 23.2 18.11 17.6 21.68 15.7 17.67 22.4 22.11 11.4 23.01 18.5 21.05 31.5 20.77 21.8 21.09 71.2 20.05 20.4 21.66 31.1 21.89 22.1 21.19 60.5 14.94 19.2 17.67 22.0 21.93 23.3 18.94 69.7 16.11 35.3 19.76 71.9 15.78 53.1 19.14 23.8 13.58 45.3 23.01 36.5 19.49 19.43 64.321.6 18.10 26.0 18.18 20.41 V 102.4 22.77 131.3 23.75 34 26 36 50 06 16 39 30 01 23 04 37 19 11 64 35 26 22 77 04 23 45 09 03 19 28 05 10 44 07 28 01 29 25 45 45 50 21 03 36 40 51 55 06 63 42 55 01 24 04 39 31 11 69 37 27 23 85 04 24 47 10 03 20 28 05 11 47 07 44 01 30 43 48 47 54 22 18 ...... 0 1 1 0 0 2 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 +0 − +1 − +1 − +0 − +0 − +2 − +0 − +1 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +1 − Table 1 Distance b Observed and Derived Properties 0.30 11,34,35 12.21 1.85 1 25.98 1.76 1 12.35 0.960.78 1 1 21.99 11.36 0.84 1 16.90 1.64 1 16.84 0.80 11 8.75 1.994.00 1 3 26.88 11.54 1.00 11,34,35 17.33 1.98 1 13.54 2.10 1 25.14 1.42 1 13.07 1.51 1 21.07 0.99 1 16.96 4.00 4 24.39 0.94 1 15.68 3.80 5 17.06 0.89 21,30 3.85 1.06 1 10.48 3.02 4 16.41 2.02 1 15.19 3.00 4 3.62 2.60 4 14.22 5.40 51.03 16.23 1 6.41 0.76 1 8.47 1.77 1 11.16 2.73 17 12.20 3.1 5 20.79 2.07 1 13.15 1.80 4 14.68 2.67 213.60 6.37 4 4.53 1.00 4 14.06 1.67 12.302.10 16.57 4 4 24.33 2.38 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± P.A. Parallax Ref. yr) (deg) (mas) (pc) (Km s μ /  0.460 129.1 48.1 0.955 160.0 70.30 b , a ··· ··· 2253 L0.5 16 0.189 038.1 38.48 1403 L2.5 15 0.195 032.5 80.95 5003 L4.5 27 1.646 286.2 59.38 3402 L0.5 15 0.158 036.5 47.46 1532 L2.0 15 0.240 146.1 58.96 1309 L1.0 28 0.578 273.0 87.96 2444 L1.5 28 0.196 135.5 45.47 2530 L2.5 28 0.889 279.2 59.15 1548 L3.0 12 0.290 288.1 57.70 3647 M8.5 18 0.690 196.0 76.46 2534 L0.0 28 0.250 289.3 63.76 61 M8.0 31 0.405 005.0 60.93 0214 M9.5 20 0.155 328.8 86.60 1222 M9.0 31 0.322 234.4 58.60 − − − − − − − − − − − 2722 M9.0 18 0.098 026.0 41.00 031 M7.0 25 0.356 028.0 95.35 021 M8.0020 15 0.274 M9.0 175.7 61.60 7 0.408 048.5 155.89 346 M7.5 18 0.409 244.0 89.54 0494B M9.5 9 0.253 089.1 39.77 0494A M6.0 24 0.253 086.5 37.20 − − − − − − − − − − 22:53:22 2MASS J0428 27:06:0037:37:44 RG 0050 LHS 132 M8.0 2216:06:57 1.479 079.8 LP 775 81.95 14:03:02 2MASS J0523 49:00:50 ESO 207 24:44:4213:09:19 DENIS J0812 SSSPM J0829 42:45:4001:58:20 LEHPM1 BRI B0021 25:30:43 DENIS J0751 50:03:55 2MASS J1126 42:44:49 LEHPM1 15:48:17 DENIS J1058 40:44:06 GJ 1001BC L4.5 14 1.643 156.0 77.02 16:51:2236:47:53 LP 771 35:25:44 DENIS J0306 00:52:45 LP 944 LHS 160434:02:15 2MASS J0451 M7.5 15 0.526 176.0 68.10 15:32:3703:29:28 2MASS J0847 LHS 206511:20:11 M9.0 LHS 292 31 0.55013:13:08 249.4 M6.0 117.98 31 LHS 2397aAB 1.64522:24:58 158.0 M8.5J12:38:36 220.30 LP 8 851 BRI B1222 0.507 264.7 65.83 25:34:50 DENIS J0652 − − − − − − − − − − − − − − − − − − − − − − − − − − − 2000 2000 Type ( 5 00:36:16.0 +18:21:10 2MASS J0036+1821 L3.5 10 0.907 082.4 114.20 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) 13 04:28:50.9 67 00:52:54.7 01:02:51.2 9 02:53:00.5 +16:52:58 SO0253+165214 M6.5 04:35:16.1 2117 5.050 05:23:38.2 137.9 259.41 19 07:07:53.3 20 07:46:42.5 +20:00:3222 2MASS J0746+2000AB 08:12:31.7 23 L0.0J 08:28:34.1 33 0.377 261.9 81.84 34 11:06:18.9 +04:28:32 LHS 2351 M7.0 34 00:21:10.7 00:24:24.6 16 05:00:21.0 +03:30:50 2MASS J0500+0330 L4.021 29 07:51:16.4 0.350 177.924 73.85 08:29:49.3 +26:46:33 GJ 1111 M6.5 31 1.290 242.2 275.80 36 11:26:39.9 2 00:21:05.8 37 11:53:52.7 +06:59:56 LHS 2471 M6.5 33 10:58:47.9 ID R.A.1 Decl. 00:04:34.9 Name Spct. Ref. 8 02:48:41.0 10 03:06:11.5 11 03:39:35.2 12 03:51:00.0 15 04:51:00.9 25 08:40:29.726 +18:24:09 08:47:28.7 27 08:53:36.0 28 09:00:23.629 GJ 316.1 +21:50:04 09:49:22.230 +08:06:45 10:48:12.8 31 10:49:03.4 M6.0 LHS32 2090 +05:02:23 10:56:29.2 LHS 32 2195 +07:00:53 0.908 M6.0 LHS35 240.0 2314 M8.0 11:21:49.0 21 71.10 GJ 406 0.774 6 M6.0 221.238 156.87 0.887 11:55:42.9 39 177.4 2 M6.0 12:24:52.2 60.32 0.624 31 217.0 4.696 41.10 235.0 419.10 18 06:52:19.7

3 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. ; ; ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· 2002 2006 .006 .004 .003 .002 .001 .002 .004 .003 .004.006 e d,f .020 d .002 .007 d,f .008 .008 .003 e .008 .012 .005 .006 d,e .004 .009 g .012 g .010 g ´ eetal. )  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± R ; (33) Konopacky 2009 ; (22) Reyl ; (11) Dahn et al. )( .026 0.173 .018 0.117 .022 0.126 .013 0.116 .008 0.147 .015 0.096 .021 0.126 .025 0.100 .007 0.120 .029 0.097 .032 0.190 .009 0.091 .033 0.126 .009 0.104 .011 0.113 .009 0.115 .030 0.120 .013 0.109 .030 0.096 .041 0.111 .029 0.094 .010 0.098 .019 0.112 .019 0.098  2006 2000 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± L/L 2.909 3.309 3.163 3.266 2.972 3.712 3.271 3.459 3.214 3.695 3.129 3.602 3.616 4.029 3.793 3.340 3.812 4.185 3.593 3.423 3.542 3.703 3.931 4.006 Luminosity Radius Notes − − − − − − − − − − − − − − − − − − − − − − − − ; (32) Shkolnik et al. 25 45 35 69 22 17 12 27 30 26 66 43 62 29 111 53 88 48 40 42 36 100 100 100 ; (10) Gizis et al. ; (21) Henry et al. ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± eff 2009 T 2000 2005 VRI c ; (31) Jenkins et al. ; (9) Basri et al. Tel. ; (20) Lodieu et al. 2009 1999 2005 .027.001 C.008 S 2.034 C 2 S 2598 2.010 2026 1 C 2508 .008 1752 2 C 2624 2.007.019 C 2581 .014 C 2.005 C 1.014 C 2718 1.015 S 2194 2.006 C 2466 2.026 C 2485 3.008 S 1925 1.021 C 2611 1.022 S 2207 2.019 S 2478 1.001 S 2179 1.001 S 1851 2 S 1567 2 2347 2 2412 2438 .018 C 2 2398 .052 S.022 1 C 2186 1.046 C 1788 1 1835 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ın et al. ´ ; (8) Mart .005 13.78 .050 16.80 .013 14.58 .041 17.35 .080 14.81 .006 12.53 .021 12.49 .019 15.82 .014 14.78 .014 15.58 .001 15.65 .015 12.25 .009 16.67 .032 12.76 .036 16.04 .023 17.18 .028 17.77 .005 16.46 .001 15.98 .001 15.89 .006 15.02 .056 15.97 .034 16.89 .035 17.56 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 1997 ; (19) Liu & Leggett ; (30) Gatewood & Coban 18.45 19.22 19.69 2005 2008 re either primary sources or, if a primary source could not be found, secondary sources that discuss spectral .063 16.15 .060 19.14 .026 17.00 .060 19.67 .026 17.04 .014 14.90 .039 14.66 .150 18.28 .024 17.19 .042 18.01 .045 17.99 .059 14.64 .032 19.04 .029 15.21 .155 18.49 .023 19.46 .039 20.26 .050 18.90 .015 18.45 .055 18.34 .021 17.39 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± left blank. VR I ··· ··· ··· ; (7) Kirkpatrick et al. ; (29) Reid et al. ; (18) Crifo et al. ) Epochs (K) log( 1 − 1997 2008 tan 2005 3.7 19.63 V 46.425.9 18.36 26.0 22.03 29.8 19.37 88.1 22.81 34.831.5 18.95 29.9 16.95 46.5 24.777.4 16.53 30.7 21.04 30.4 19.49 45.9 20.23 36.7 20.96 14.2 16.85 39.7 21.67 24.7 17.68 59.2 21.14 53.7 22.37 46.5 23.82 53.9 21.36 28.2 20.96 20.81 50 55 27 11 10 53 23 08 06 32 07 21 35 50 10 02 56 01 83 58 09 69 01 60 53 58 28 11 10 56 24 08 06 34 07 22 36 53 10 02 59 01 89 62 09 74 11 64 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 Table 1 +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − (Continued) Distance ; (17) Costa et al. ; (6) Gizis & Reid b ; (28) Phan-Bao et al. 2003 1996 2008 1.76 1 18.15 1.21 1 13.41 0.82 1 11.09 1.11 1 22.22 0.83 1 11.56 1.71 10.60 11.78 11 10.59 1.471.48 1 1 15.64 18.75 1.710.69 1 111.57 18.86 11.53 11.71 21.46 1 19.09 1.72 1 17.31 1.26 1 16.32 0.50 11 14.36 1.50 1 23.96 2.02 4 6.55 0.70 1 10.56 1.54 11 19.23 0.50 26 5.84 2.09 1 22.53 0.52 26 6.45 1.33 1 14.42 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ; (5) Tinney 1995 ; (16) Kendall et al. ; (27) Looper et al. 2003 P.A. Parallax Ref. 2007 yr) (deg) (mas) (pc) (Km s μ /  0.566 125.8 57.77 b , a ; (4) van Altena et al. ; (15) Cruz et al. ··· 1995 ; (26) van Leeuwen 2002 2007 . . V 2012 0956 L1.0 131319 1.217 L1.5 129.9 74.53 13 0.874 203.8 90.12 10370158 L3.0 L4.5 15 11 0.662 116.0 0.984 53.00 152.3 86.70 5009 M9.03426 20 M9.0 0.458 082.7 20 46.59 0.312 167.1 52.37 3650 L3.0 296604 0.544 L3.5 211.6 86.45 28 0.565 125.1 84.88 0520 L3.5 25 0.602 079.9 61.25 ; (3) Tinney et al. 04420631 M8.0 M7.0 13 13 0.415 180.2 0.342 63.90 176.3 53.31 6332 M9.0 25 0.218 158.0 41.72 0516AB L0.5 23 0.165 132.5 55.07 − − − − − − − − − 0174 M6.5 excludes − − − − − ; (14) Leggett et al. eff 1995 T ; (25) Schmidt et al. 2002 2007 ; (35) Faherty et al. 2012 ; (13) Gizis et al. . 8 21:21:09 LEHPM2 28:09:51 LHS 300326:23:07 M7.0 LHS 5303 17 0.965 M6.0 210.0 152.49 18 0.495 155.1 94.63 25:41:0636:50:22 Kelu-1AB DENIS J1425 66:04:47 L2.0J 19 DENIS J1454 0.285 272.2 52.00 09:56:0504:42:06 2MASS J1555 06:31:45 SIPS J1607 13:19:51 SIPS J1632 2MASS J1645 05:16:46 2MASS J1705 05:20:43 DENIS J1539 23:30:33 CE 303 M7.0 13 0.381 176.0 69.33 08:23:40 GJ 644C63:32:0510:37:37 SIPS J2045 01:58:52 2MASS J2104 M7.050:08:58 2MASS J2224 1733:16:25 SSSPM J2307 34:26:04 1.202 223.4 SSSPM LHS J2356 154.96 4039C M9.0 29 0.505 218.3 44.38 ; (24) Caballero 2002 − − − − − − − − − − − − − − − − − − − − 2006 ; (34) Dupuy & Liu 2000 2000 Type ( photometry is available. SED fit and 2010 V References: (1) This work; (2) Reid et al. See notes in Section No Unfortunately many papers do not cite references for spectral types. We have made an effort to track down primary sources. The references listed here a S - SOAR; C - CTIO 0.9 m. Member of resolved multiple system. Parallaxes for 1, 55, and 57 are for brighter components. Unresolved multiple. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) typing. In a few cases, several papers list the same spectral type with no reference and do not discuss the spectral type. In these cases, this column was (This table is also available in machine-readable and Virtual Observatory (VO) forms in the online journal.) ID R.A.40 12:50:52.2 Decl. Name Spct. Ref. Notes. a b c d e f g 45 14:40:22.9 +13:39:2347 14:56:38.5 2MASS J1440+1339 M8.050 25 15:52:44.4 0.331 204.7 45.00 41 13:05:40.2 43 14:25:27.9 46 14:54:07.9 48 15:01:07.9 +22:50:02 2MASS J1501+225051 15:55:15.7 52 M9.0 16:07:31.3 53 31 16:32:58.8 54 0.074 16:45:22.1 211.756 94.40 17:05:48.3 57 19:16:57.6 +05:09:02 GJ 752B M8.0 31 1.434 203.8 171.20 49 15:39:41.9 42 13:09:21.9 44 14:39:28.4 +19:29:15 2MASS J1439+1929 L1.0 11 1.295 288.3 69.60 55 16:55:35.3 58 20:45:02.3 59 21:04:14.9 60 22:24:43.8 61 23:06:58.7 62 23:54:09.3 63 23:56:10.8 (12) Geballe et al. (23) Reid et al. et al.

4 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. and Graham (1982). In each night, at least two standards were most relevant for the observation of very red and faint targets is red standards with V − I>3.0. Details of the transformation given here. equations used to derive the nightly photometric solution from Each target was typically observed for five “evening” epochs the observation of photometric standards are given in Jao et al. (i.e., before the midpoint of a given night) and five “morning” (2005). epochs over the course of at least two . Observations were After flat fielding, bias subtraction, and mosaic integration typically taken in sets of three consecutive 600 s exposures in the case of SOAR/SOI images, we performed aperture always within ±60 minutes of target transiting, and in most photometry using the IRAF apphot package. Landolt standards cases within ±30 minutes of transiting. This restriction in hour are reduced using an aperture 7 in radius. Ideally, we would angle means that the target is always observed very close to perform aperture photometry on our targets using the same its lowest possible air mass, which minimizes the effects of size aperture (7) as Landolt used to compile the standards differential atmospheric refraction. All but one target were we are using, but the faintness of our targets required us to observed in the I band, where their optical spectrum is the use a smaller aperture for two reasons. First, the depth of brightest and also where atmospheric refraction is minimized. our exposures (as faint as V ∼ 24 at SOAR and V ∼ 21 The sole exception is GJ 1001 A-BC, for which the parallax at the CTIO 0.9 m; see Section 6.1) means that the science of the A component was measured in the R band to avoid target is often not more than 7 apart from another source. saturation. The long exposures caused the fields to be rich Second, the signal-to-noise error associated with a photometric with background stars, which greatly facilitated the selection observation is a combination of the Poisson error and the sky of parallax reference stars. In most cases, we were able to subtraction error. The latter’s contribution is proportional to the set up the parallax field with the ideal configuration of ∼10 area of the photometric aperture and is particularly problematic reference stars symmetrically distributed around the science in deep exposures where the sky annulus may contain diffuse target. Care was taken to position the reference fields using the background sources. It, therefore, makes sense to use a smaller same pixel coordinates for all epochs. Our experience shows that aperture and apply an aperture correction based on the curve this consistency of positioning the reference fields helps reduce of growth of bright stars in the same exposure. We used a the final parallax error faster but is not absolutely required. There 3 aperture with an aperture correction to 7. The uncertainty have been instances when a misaligned was added to the associated with this aperture correction depends strongly on the parallax reduction, and having an additional epoch, although seeing but is typically on the order of 1% to 3%. The final not perfectly positioned, still reduced the parallax error. Such photometric error is the sum in quadrature of the signal-to-noise instances were considered on an individual basis. error, the error due to the aperture correction, and the error from VRI photometry (see Section 3) of the reference field was used the nightly photometric solution, which is typically on the order to transform the relative parallaxes into absolute parallaxes using of 1% to 2%. Each photometric night had at least two targets in photometric distance relations. This transformation accounts overlap with another night in order to check the validity of the for the fact that the parallax reference stars are not located at night’s photometric solution. We discuss optical variability in infinite distances and therefore have a finite, albeit much smaller, Section 6.5, where we show that the variability is usually less parallax. Any original reference star later found to be closer than than the formal uncertainty in the photometry, thus justifying 100 pc was discarded. The VRI photometry of the reference field the use of only one epoch of photometry in cases where we and the science star was also used to correct for small shifts in were unable to obtain a second epoch due to time constraints on the apparent positions of the stars due to atmospheric differential SOAR. color refraction. Several different UBVRI photometric systems are in current usage. While the photometry taken on the CTIO 0.9 m telescope 5. METHODOLOGY FOR CALCULATING EFFECTIVE used filters in the Johnson–Kron–Cousins system, data taken on TEMPERATURES AND LUMINOSITIES SOAR used Bessell filters. Descriptions of both systems, as Determining the effective temperatures (T )6 of M and L well as conversion relations, are given in Bessell (1995). The V eff dwarfs has traditionally been difficult due to the complex nature filter is photometrically identical between both systems. The R of radiative transfer in cool stellar atmospheres. The task is and I filters have color dependent differences that reach a few particularly challenging in the L dwarf regime, where inter- percent in the color regime explored by Bessell (1995), which phase chemistry between solid grains and the same substances considered stars as red as (V −R) = 1.8 and (V −I) = 4.0. The in the gas phase becomes relevant. Significant progress has targets in this study are significantly redder, with (V − I)asred occurred recently with the publication of the BT-Settl family as 5.7. In Section 6.1, we derive new relations relevant to the very of model atmospheres (Allard et al. 2012, 2013). The BT-Settl red regime considered in this study. The values listed in Table 1 models are the first to include a comprehensive cloud model are on the system used on each telescope (see Section 6.1). based on non-equilibrium chemistry between grains and the 4. ASTROMETRIC OBSERVATIONS gas phase and the rate of gravitational settling of solid grains. They have also been computed using the latest revised solar The Cerro Tololo Inter-American Observatory Parallax Inves- (Caffau et al. 2011). The authors (e.g., Allard et al. tigation (CTIOPI; Jao et al. 2005; Henry et al. 2006)isalarge 2012) have demonstrated unprecedented agreement between and versatile astrometric monitoring program targeting diverse observed M and L spectra and the BT-Settl model atmospheres. types of stellar and substellar objects in the solar neighborhood. We determined Teff for each object in our sample by com- Observations are taken using the CTIO 0.9 m telescope and its paring observed photometric colors to synthetic colors derived sole instrument, a 2048 × 2048 Tektronix imaging CCD de-  − 6 tector with a plate scale of 0.401 pixel 1. We use the central The (Teff ) of a surface is defined as the temperature at  ×  which a perfect blackbody would emit the same flux (energy per time per area) quarter of the CCD chip, yielding a 6.8 6.8 field of view. 4 as the surface in question according to the Stefan–Boltzmann law: F = σSBT . Details of the observing procedures and data reduction pipeline This quantity often differs from the stellar atmosphere’s actual temperature, are given in Jao et al. (2005). A brief description of the aspects which is a function of optical depth as well as other factors.

5 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

Table 2 Photometric Properties of Individual Bands

Band Blue Limita Red Limita Effective Isophotal λ Mag. Zero Point Reference (μm) (μm) (μm) (photon s−1 cm−2) V 0.485 0.635 0.545 1.0146 × 1011 Bessell & Murphy (2012) R 0.554 0.806 0.643 7.1558 × 1010 Bessell & Murphy (2012) I 0.710 0.898 0.794 4.7172 × 1010 Bessell & Murphy (2012) J 1.102 1.352 1.235 1.9548 × 1010 Cohen et al. (2003) H 1.494 1.804 1.662 9.4186 × 109 Cohen et al. (2003) 9 Ks 1.977 2.327 2.159 4.6692 × 10 Cohen et al. (2003) W1 2.792 3.823 3.353 1.4000 × 109 Jarrett et al. (2011) W2 4.037 5.270 4.603 5.6557 × 108 Jarrett et al. (2011) W3 7.540 16.749 11.560 3.8273 × 107 Jarrett et al. (2011)

Note. a 10% transmission normalized to band’s peak transmission. from the BT-Settl model grid using custom made IDL proce- no apparent systemic trend. We therefore performed the calcu- dures. Our procedure exploits the fact that synthetic colors can lations a second time using only the colors involving the VRI be computed from synthetic spectra and those colors can then be bands and excluding I−J, which also did not converge well, for directly compared to observed colors. How well the synthetic a total of twenty colors. Occasionally, a color combination still colors match the observed colors is then a measure of how produced an outlier at Teff 2σ from the adopted value. These well the input properties of a given synthetic spectrum (Teff, outliers were excluded as well; however, the majority of ob- log g, and [M/H]) match the real properties of the object in jects had their effective temperatures computed using all twenty question. The best matching Teff can then be found by interpo- colors. The fact that none of the colors composed of infrared lating Teff as a function of the residuals of the color comparison bands alone had good convergence emphasizes the need to in- (observed color − synthetic color) to the point of zero residual. clude optical photometry when studying VLM stars and brown The technique can be applied independently to each available dwarfs. photometric color, and the standard deviation of the resulting The model grid we used was a three-dimensional grid with a ensemble of Teff values is the measure of the uncertainty in Teff. Teff range from 1300 K to 4500 K in steps of 100 K, log g range In our implementation of this technique, we first com- from 3.0 to 5.5 in steps of 0.5 dex, and metallicity, [M/H], range bined our VRI photometry (Bessel system) with 2MASS JHKs of −2.0 to 0.5 in steps of 0.5 dex. The procedure was repeated (Skrutskie et al. 2006) and WISE W1, W2, and W3 photome- for each different combination of log g and [M/H]. The final try (Wright et al. 2010) to derive a total of 36 different colors adopted Teff was the one from the combination of gravity and for each object covering the spectral range from ∼0.4 μmto metallicity that yielded the lowest Teff dispersion amongst the ∼16.7 μm.7 We then calculated the same 36 colors for each colors. As expected for VLM stars and brown dwarfs in the spectrum in the BT-Settl model grid using the photometric prop- solar neighborhood, the vast majority of objects had their best erties for each band listed in Table 2.8 fit effective temperatures at log g = 5.0 and [M/H] = 0.0. The For each color, we then tabulated the residuals of (observed color–Teff interpolations often did not converge for grid points color − synthetic color) as a function of the synthetic spec- where log g or [M/H] was more than 1.0 dex away from the trum’s temperature. The residuals are negative if the synthetic final adopted value. We reserve a comprehensive discussion of spectrum’s temperature is too cold, approach zero for spectra metallicity and gravity issues in our observed sample for a future with the right temperature, and are positive for models hotter publication reporting our spectroscopic observations. than the science object. For each color, we then interpolated the The IDL procedure for determining effective temperatures residuals as a function of temperature to the point of zero resid- also indicates which model spectrum in the BT-Settl grid ual. The temperature value of this point was taken as the object’s provides the overall best fit to the observed photometry. We effective temperature according to the color in question. We then used the indicated best fit spectrum as a template for an object’s repeated the procedure for all 36 color combinations, thus pro- SED in order to calculate an object’s luminosity. Because the viding 36 independent determinations of Teff. The adopted Teff model spectra are spaced in a discrete grid, and because no for each object is the mean of the Teff values from each color. model spectrum can be expected to provide a perfect match to The uncertainty in Teff is the standard deviation of the values observations, significant differences may still remain between used to compute the mean. After performing this procedure, the best fit synthetic spectrum and the real SED. We devised we noted that the majority of colors produced Teff results that an iterative procedure that applies small modifications to the converged in a Gaussian fashion about a central value, while chosen SED template in order to provide a better match to other colors produced outliers that were a few hundred the photometry. We first calculated synthetic photometry from away from the Gaussian peak. Further inspection showed that the SED template for all nine bands listed in Table 2 using a colors for which the bluest band was an optical band (VRI)were procedure identical to the one used for calculating synthetic producing the convergent results while colors in which both colors for the purpose of Teff determination. We then did a bands were infrared bands tended to produce erratic values with band by band comparison of the synthetic photometry to the observed photometry and computed a corrective flux factor by 7 We did not use the WISE W4 band centered at ∼22 μm because it produces dividing the flux corresponding to the observed photometry by mostly null detections and upper limits for late M and L dwarfs. the synthetic flux. Next, we paired the corrective flux factors to 8 A thorough review of photometric quantities, terminology, and procedures for deriving synthetic colors is given in the appendix of Bessell & Murphy the corresponding isophotal effective wavelength for each band (2012). and fit those values to a ninth order polynomial using the IDL

6 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. function poly_fit, thus creating a continuous corrective function with the same wavelength coverage as the SED template. While it may seem unusual to fit nine bands of photometry to a ninth order polynomial, we note that the purpose of the fit is not to follow the general trend in the data, but rather to provide corrections to each individual band while still preserving the continuity of the SED. It therefore makes sense to use a function with the same order as the number of data points. To facilitate computations, poly_fit was run on a logarithmic wavelength scale that was then transformed back to a linear scale. The original SED template was then multiplied by the corrective function and the process was iterated until residuals for all bands fell below 2%. Because the W3 band is much broader than the other bands, two additional points were used to compute the corrective function at the blue and red ends of the band as well as at the isophotal wavelength. Figure 2 describes the process (a) graphically. The first iteration typically produced mean color shifts of 0.1 to 0.25 mag, depending on how well the real SED of a given object matched the closest point in the spectral template grid. The BT-Settl models are published with flux units as they ap- pear at the stellar surface. These are very high fluxes when com- pared to observed fluxes on Earth. To facilitate computations, the model spectra were first normalized to a value that is com- parable in magnitude to the observed photometric fluxes that are used to calibrate the spectrum. Given the range of magnitudes of our objects, we found that normalizing the model spectra so that their bolometric flux is 10−10 erg s−1 cm−2 works well. The first iteration corrected for the bulk of the flux mismatch between the real target and this arbitrary normalization, thus causing a much larger correction than the subsequent iterations. The number of iterations necessary for conversion varied greatly, ranging any- where from three to twenty or more. Table 3 shows the overall (b) corrective factor for each band for the three examples shown in Figure 2, as well as the number of iterations that were neces- sary. The flux factors in Table 3 were normalized to 1.000 at the H band for ease of comparison. To check that our correc- tive polynomial approach was producing consistent results, we computed the luminosities for the objects listed in Table 3 using ninth order polynomials as well as eighth order polynomials. The results of dividing the luminosity obtained using the eighth order polynomials by that obtained using ninth order polyno- mials were 1.00052, 1.00077, and 0.99451, respectively, for LHS 3003, 2MASS J1501+2250, and 2MASS J2104−1037. The uncertainties associated with the adopted ninth order so- lution are 3.08%, 1.91%, and 6.97%, respectively, for LHS 3003, 2MASS J1501+2250, and 2MASS J2104−1037. This test shows that so long as the polynomials used are of high enough order, varying the order of the corrective polynomial causes changes to the resulting luminosities that are well within (c) the formal uncertainties. Figure 2. SED calibrations for (a) LHS 3003 (M7V), (b) 2MASS J1501+2250 The uncertainty in the final flux under the SED was calculated (M9V), and (c) 2MASS J2104−1037 (L3). The corrective polynomial functions are shown by dashed lines and are fits to the corrective factors shown by plus by propagating the uncertainty in the observed photometry and signs. In the first two cases, the polynomial generated in the first iteration stands the residuals of the final SED fit for each band and summing the out at the bottom of the graph due to the flux mismatch caused by the difference results in quadrature. Finally, the total flux was divided by the between the object’s real distance and the distance at which the SED template fraction of a blackbody’s total flux covered by the SED template was calculated. The first iteration is too close to the wavelength axis to be given the effective temperature of the object in question. This noticeable in (c). The following iterations then produce corrective functions that differ only slightly from a flat 1.0 function and perform a “fine tuning” of correction accounted for the finite wavelength range of the SED the modifications caused by the first iteration. Both the original SED template and was typically on the order of 1.5%. and the final fit are plotted normalized to 1 at their maximum values. In the Once the effective temperatures and the observed bolo- cases of 2MASS J1501+2250 and 2MASS J2104−1037, the end result is an metric fluxes were determined by the procedures described SED slightly redder than the template. The template used for LHS 3003 was a very good fit and the resulting SED almost entirely overlaps the initial template. above, determining the radii of stars or brown dwarfs with Table 3 lists the cumulative correction factors applied to each band for the three a known trigonometric parallax followed easily from the objects in this figure.

7 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

Table 3 Corrective Factors for SEDs Shown in Figure 2a

Object Iterations VR I JHKs W1 W2 W3 LHS 3003 22 0.865 0.917 0.927 0.952 1.000 1.044 1.042 1.002 0.711 2MASS J1501+2250 3 1.144 1.037 0.986 0.911 1.000 1.113 1.203 1.201 1.032 2MASS J2104−1037 3 1.031 1.066 1.028 0.931 1.000 1.033 0.842 0.724 1.075

Note. a All values are normalized to 1.000 in the H band.

6. RESULTS Table 1 includes astrometric results (our new values as well as values from the literature), our VRI photometry, and the derived effective temperatures, luminosities, and radii for all objects. Table 4 reports detailed astrometric results for the 37 objects for which we report new trigonometric parallaxes. All resulting quantities are synthesized and summarized graphically in Figure 4, a bona fide HR diagram for the end of the stellar main sequence. We discuss several auxiliary results separately here and save a thorough discussion of the structure of the stellar/substellar boundary for Section 7. 6.1. Photometric Results Columns 13–17 of Table 1 list our VRI photometry, the telescope in which the photometry was taken, and the number of epochs for which each target was observed. For the 28 targets observed on both telescopes, Table 1 lists the set of observations with the smallest error or the most epochs, with the number of epochs taking priority in selecting which data set to adopt. The electronic version of Table 1 lists both sets of photometry for these objects, along with 2MASS JHKs and WISE W1W2W3 photometry for all objects. We achieved Figure 3. Comparison of M dwarf radii obtained via our SED fitting technique sensitivities of V = 23.75 ± 0.01 on SOAR with 90 minute to values based on direct angular diameter measurements obtained with Georgia exposures under dark skies and good seeing. The time demands State University’s CHARA Array Optical Interferometer (Boyajian et al. 2012). From smallest to largest, the points correspond to: Barnard’s Star (M4.0V), of the CTIOPI program at the 0.9 m telescope forced us to GJ 725B (M3.5V), GJ 725A (M3.0V), GJ 15A (M1.5V), GJ 411 (M2.0V), GJ limit exposures to 20 minutes for the majority of targets. Under 412A (M1.0V), and GJ 678 (M3.0V). The percent residuals in the sense (SED dark skies and good seeing (i.e., 1.0) 20 minute integrations fit − CHARA) are: −0.3%, −10.9%, −3.6%, 0.8%, −1.3%, −1.3%, and 5.3%, yielded results as faint as V = 19.50 ± 0.05. In exceptional respectively. The mean absolute residual is 3.4%. cases when we took longer integrations, we were able to achieve V = 21.93±0.07 in 90 minutes under extraordinary conditions. Stefan–Boltzmann law: The majority of the measurements had errors <0.05 mag (i.e., 5%); however, for the fainter 0.9 m observations, the errors are as large as 0.15 mag. It was our original intention to observe = 2 4 L 4πR σSBTeff all targets for at least two epochs, but this was not possible for some targets due to time constraints on SOAR. As discussed in where L is the object’s luminosity, R is its radius, σSB = Section 6.5, the optical variability for the sample is comparable 5.6704 × 10−5 erg cm−2 s−1 K−4 is the Stefan–Boltzmann to the photometric error, meaning that single epoch photometry constant, and Teff is the effective temperature. should be generally consistent with the values we would obtain In order to check the accuracy of our procedures for de- by averaging more observations. termining effective temperatures and luminosities, we applied Table 1 shows the photometry in the photometric system our methodology to seven M dwarfs that have direct model- used by the telescope with which the measurements were independent radius measurements obtained using Georgia State taken—Johnson–Kron–Cousins for the CTIO 0.9 m telescope University’s CHARA Array Long Baseline Optical Interferom- and Bessell for SOAR. We have also converted the CTIO 0.9 m eter (Boyajian et al. 2012). Figure 3 shows the comparison. The values to the Bessell system, and we present these data in the mean absolute residual is 3.4%. While it is currently difficult to electronic version of Table 1. Rather than extrapolating the directly measure the angular diameters of late M and L dwarfs relations of Bessell (1995), we used the 28 objects observed using interferometry, the good agreement we obtain when com- on both telescopes to derive new relations between the colors paring the results of our SED fitting procedure to direct radius (V − RB ) and (V − RC )aswellas(V − IB ) and (V − IC ) and measurements for hotter M dwarfs serves as a check on our show the results in Figure 5. Given the photometric uncertainties technique. We also note that while direct radius measurements of our V and R observations (typically 5%; Table 1), we exist for several eclipsing binaries, the individual components find no systematic deviation between the two (V − R) colors. of these systems lack the photometric coverage needed for ap- We therefore adopt RB = RC for the purpose of this study. plying our method and therefore cannot be used as checks. We do detect a trend in the (V − I) colors, as shown in

8 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. d ··· Var. ) (mmag) 1 − tan V .25 31.5 19.9 .28 34.8 6.9 .04 102.4 .17 46.5 17.0 .12 69.7 11.1 .17 29.8 15.1 .53 30.1 15.4 1.11 23.2 18.0 .40 53.9 20.0 .08 45.9 11.6 .53 32.2 6.5 .05 24.7 10.7 .31 18.5 10.5 .79 14.2 40.9 .11 36.5 22.1 .11 17.6 8.1 .16 42.7 8.4 .09 71.2 15.3 .67 28.2 10.2 .88 24.7 38.9 .06 131.3 25.3 .07 12.4 8.8 .12 77.4 9.9 .75 15.7 50.6 .41 22.4 14.8 .41 20.4 19.9 .23 21.6 10.4 .26 30.7 12.2 .94 11.4 11.7 .10 31.1 9.2 .22 59.2 12.5 .15 46.4 7.8 .26 26.0 10.2 .34 19.2 9.9 .04 22.0 12.1 .32 46.5 11.5 .45 30.4 17.9 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± P.A. ) (deg E. of N.) (Km s 1 1.3 125.1 0.9 204.7 0.6 156.0 1.1 79.9 1.2 177.4 0.8 211.6 1.6 089.1 1.9 038.1 0.6 203.8 1.5 086.5 0.2 155.1 1.1 132.5 0.6 264.7 0.4 028.0 1.1 196.0 0.8 279.2 2.1 167.1 1.2 158.0 1.0 286.2 0.3 048.5 1.3 129.9 1.0 036.5 1.7 177.9 0.7 135.5 0.9 244.0 1.2 180.2 1.6 032.5 0.7 273.0 1.3 116.0 0.6 125.8 1.1 176.0 0.7 146.1 0.2 249.4 0.7 289.3 1.6 82.7 1.9 176.3 1.8 218.3 − ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± μ 1.71 564.8 1.11 331.1 2.07 1643.6 1.26 602.3 1.67 886.7 0.83 543.7 2.10 252.9 1.85 189.3 0.82 873.8 1.99 252.8 0.70 495.4 1.76 164.7 2.02 506.9 1.06 356.0 1.42 690.0 0.84 889.1 1.71 312.5 1.50 220.4 1.64 1645.7 1.03 408.3 1.21 1217.0 1.51 157.6 1.98 350.2 0.96 196.4 1.77 408.6 1.47 414.6 1.76 194.5 0.78 577.3 1.71 661.9 1.72 565.7 1.33 380.5 0.99 239.5 0.76 550.3 0.94 249.6 1.57 457.8 1.48 342.2 2.09 505.5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± (abs) π 0.17 84.88 0.07 45.00 0.16 77.02 0.08 61.25 0.15 60.32 0.24 86.45 0.08 39.77 0.04 38.48 0.10 90.12 0.08 37.20 0.07 94.63 0.26 55.07 0.07 65.83 0.13 95.35 0.08 76.46 0.02 59.15 0.07 52.37 0.07 41.72 0.12 59.38 0.10 155.89 0.05 74.53 0.47 47.46 0.12 73.85 0.03 45.47 0.06 89.54 0.06 63.90 0.10 80.95 0.16 87.96 0.15 53.00 0.03 57.77 0.14 69.33 0.09 58.96 0.03 117.98 0.04 63.76 0.06 46.59 0.14 53.31 0.15 44.38 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ates a continuous set of observations where multiple nights of data were taken in each (corr) π s are better. 1.70 0.67 1.11 0.87 2.06 1.03 1.26 0.74 1.66 0.77 0.79 0.65 2.10 0.55 1.85 0.44 0.81 0.93 1.99 0.55 0.70 0.53 1.74 1.73 2.02 0.55 1.05 0.82 1.42 0.67 0.84 0.50 1.71 0.57 1.50 1.07 1.64 0.56 1.03 1.36 1.21 0.59 1.43 1.03 1.98 0.47 0.96 0.68 1.77 0.62 1.47 1.11 1.76 0.60 0.76 0.72 1.70 0.77 1.72 0.44 1.32 0.92 0.99 0.62 0.76 0.79 0.94 0.52 1.57 0.38 1.47 1.00 2.08 2.47 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± (rel) π c ref N Table 4 2013.26 3.94 11 84.21 2013.26 4.01 8 44.13 2011.74 12.10 6 75.99 2013.25 4.00 11 60.51 2013.28 3.96 13 85.80 2012.83 3.97 9 39.22 2012.94 2.92 9 38.04 2012.83 3.97 9 36.65 2012.59 8.02 10 94.10 2013.25 3.93 10 53.34 2013.26 8.16 9 65.28 2012.88 8.94 8 94.53 2012.94 3.19 8 75.79 2013.12 2.97 10 58.65 2011.77 2.21 9 51.80 2013.54 2.95 11 40.65 2013.25 4.07 13 58.82 2012.94 8.99 10 154.53 2013.28 3.08 10 73.94 2013.12 4.26 8 46.43 2012.89 3.15 13 73.38 2013.25 3.24 14 44.79 2013.28 6.10 9 88.92 2013.26 2.87 8 62.79 2013.12 2.14 9 80.35 2013.26 3.32 10 87.24 2012.58 3.02 12 52.23 2013.38 8.25 9 57.33 2013.27 3.11 11 68.41 2013.27 3.95 12 58.34 2013.26 9.31 6 117.19 2013.10 3.09 9 59.55 2013.12 3.10 12 63.24 2012.81 3.26 9 46.21 2012.58 2.39 11 52.31 2007.74 4.23 5 41.91 2013.27 3.95 15 89.19 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − Coverage Years b from color–magnitude relations. frm N V New Trigonometric Parallaxes, Proper Motions, and Optical Variability a sea 5s 22 2009.32 5s 34 2009.25 5s 33 2009.31 5s 24 2008.86 5s 24 2008.86 9s 85 2004.57 5s 18 2009.32 4s 39 2009.75 5s 20 2009.19 8s 59 2003.95 5s 22 2008.86 4s 28 2010.02 7s 56 2007.18 4s 22 2010.01 8s 45 2005.14 4s 47 2010.16 5s 35 2009.32 4s 36 2010.01 5c 29 2009.25 7c 68 2005.09 7c 74 2003.95 4c 35 2010.15 3c 28 2009.56 4c 45 2010.59 4c 25 2010.19 4c 23 2009.75 4c 32 2010.39 3c 24 2010.98 4c 24 2009.94 4c 22 2009.56 4c 36 2010.02 4c 41 2009.55 3c 40 2010.19 4c 58 2003.51 5c 48 2009.32 10s 112 1999.64 10s 101 2003.95 N I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I R 66:04:47 05:20:43 40:44:06 36:50:22 42:44:49 13:13:08 42:45:40 26:23:07 16:06:57 05:16:46 25:30:43 34:26:04 63:32:05 36:47:53 09:56:05 50:03:55 35:25:44 34:02:15 24:44:42 22:24:58 04:42:06 14:03:02 13:09:19 10:37:37 22:53:22 21:21:09 23:30:33 25:34:50 15:32:37 03:29:28 50:08:58 06:31:45 33:16:25 13:19:51 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − 2000.0 2000.0 (mas) (mas) (mas) (mas yr 14:54:07.9 15:39:41.9 e e 0956 15:55:15.7 5003 11:26:39.9 3402 04:51:00.9 1403 05:23:38.2 1037 21:04:14.9 2253 04:28:50.9 1532 08:47:28.7 1319 16:45:22.1 3426 23:56:10.8 1309 08:28:34.1 5009 23:06:58.7 3650 14:25:27.9 2530 07:51:16.4 3647 03:06:11.5 2444 08:12:31.7 2534 06:52:19.7 6604 0520 6332 20:45:02.3 0442 16:07:31.3 0631 16:32:58.8 0516AB 17:05:48.3 − − − − − − − − − − − − − − − − 0174 12:50:52.2 − − 031 04:35:16.1 020 03:39:35.2 346 11:55:42.9 0494B 00:21:05.8 0494A 00:21:10.7 − − − − − − − − − − photometry. Correction for differential color refraction based on estimated V Total number of images used in reduction. Images are typically takenPhotometric in variability sets of of the three science consecutive target. observations. Number of reference stars used to reduce the parallax. No Number of seasons observed, where 2–3 months of observations count as one season, for seasons having more than three images taken. The letter “c” indic season, whereas an “s” indicates scattered observations when one or more seasons have only a single night of observations. Generally “c” observation 46 DENIS J1454 ID1 Name GJ 1001BC R.A. 00:04:34.9 Decl. Filt. Notes. a b c d e 45 2MASS J1440+1339 14:40:22.9 +13:39:23 2 LEHPM1 49 DENIS J1539 14 LP 775 56 2MASS J1705 35 LHS 2397aAB 11:21:49.0 3 LEHPM1 50 LHS 5303 15:52:44.4 21 DENIS J0751 63 SSSPM J2356 58 SIPS J2045 10 DENIS J0306 51 2MASS J1555 36 2MASS J1126 11 LP 944 15 2MASS J0451 22 DENIS J0812 38 LP 851 52 SIPS J1607 16 2MASS J0500+0330 05:00:21.0 +03:30:50 17 2MASS J0523 23 SSSPM J0829 59 2MASS J2104 13 2MASS J0428 40 LEHPM2 18 DENIS J0652 26 2MASS J0847 61 SSSPM J2307 53 SIPS J1632 27 LHS 2065 08:53:36.0 42 CE 303 13:09:21.9 43 DENIS J1425 29 LHS 2195 09:49:22.2 +08:06:45 62 LHS 4039C 23:54:09.3 54 2MASS J1645

9 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

This paper Literature

Figure 4. HR diagram for objects with spectral types ranging from M6V to L4.5. Several representative objects are named. Known binaries with joint photometry are enclosed in open circles. A few known binaries are clearly over-luminous, denoting their low luminosity ratios. The L4.5 binary GJ 1001BC was deconvolved based on the nearly identical luminosity of both components (Golimowski et al. 2004a). As we discuss in Section 7, the L2.5 dwarf 2MASS J0523−1403 lies at a pronounced minimum in the radius–luminosity relation and its location likely constitutes the end of the stellar main sequence. Versions of this diagram that use the ID labels in Table 1 and spectral type labels for plotting symbols are available as supplemental online material. (An extended, color version of this figure is available in the online journal.)

Figure 5(b). Based on the data shown in Figure 5(b), we derive a distance error of ∼1% at 10 pc and ∼3.5% at our original the transformation distance horizon of 25 pc. When comparing our results to other samples observed by CTIOPI, we found that nearby late M − =− − 2 − − (V IB ) 0.0364(V IC ) +1.4722(V IC ) 1.3563. and early L targets tend to be ideal targets for optical parallax investigations on one meter class telescopes. Although the in- We emphasize that the relations we derive here are based on a trinsic faintness of the targets made them a challenge in nights small sample and serve the purposes of our study only. They with poor seeing or a bright moon, the parallax solution con- should not be used as general relations analogous to those of verged with fewer epochs and had smaller errors than what we Bessell (1995). In particular, the difference in the I band is experience for brighter samples. We suspect that several fac- likely dominated by the different detector efficiencies between tors contribute to this good outcome. First, the long exposures the CTIO 0.9 m and the SOAR/SOI CCDs in the far red. The I average out short atmospheric anomalies that may cause asym- photometry listed in Table 1 is in the photometric system of the metric point-spread functions (PSFs). The resulting symmetric telescope that took the adopted observations. PSF profiles facilitate centroiding. Second, the long exposures We note that the procedure for determining effective tempera- generate images rich in background stars that are likely more tures and luminosities described in Section 5 uses photometry in distant than reference stars available in shorter exposures. Be- the Bessell system because the transmission curves for Bessell cause exposure times for brighter targets are often limited by the filters are well-characterized (Bessell & Murphy 2012). time it takes for the science target to saturate the detector, these 6.2. New Trigonometric Parallaxes faint and distant reference stars are not available for brighter parallax targets. Third, as already mentioned, the use of the As reported in Table 4, our trigonometric parallax measure- I band minimizes atmospheric refraction when compared to ments have a mean uncertainty of 1.43 mas, corresponding to other optical bands.

10 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. in the parallax ellipse’s eccentricity. An object with coordinates close to the ecliptic pole produces a parallax ellipse that is nearly circular, and in that case low parallax factor observations can still provide significant constraints to the parallax solution (e.g., object 1). The opposite occurs with the high eccentricity parallax ellipses for objects lying close to the ecliptic plane, where low parallax factor observations contribute little toward the final solution (e.g., object 29). Regardless of the target’s position on the celestial sphere, we found out that attempting to fit a parallax ellipse to more than ∼4 epochs but fewer than ∼7 epochs will often produce an er- roneous answer whose formal uncertainty is also unrealistically small. True convergence of a parallax result was best deter- mined by assuring that the following conditions were met: (1) adding new epochs caused changes that were small compared to the formal uncertainty; (2) high parallax factor observations were taken during both evening twilight and morning twilight; (a) and (3) the parallax ellipses shown in Figure 6 appeared to be sufficiently sampled so that the points trace out a unique ellipse. Nine of the 37 targets listed in Table 4 have previously published trigonometric parallaxes. These targets are listed in Table 5 with our new trigonometric parallax and the previous value. In five cases trigonometric parallaxes were not yet published at the beginning of this study in 2009 (Andrei et al. 2011; Dupuy & Liu 2012; Faherty et al. 2012). LHS 4039C (Subasavage et al. 2009) is a member of a resolved triple system; we re-reduced our data set with LHS 4039C as the science target (see Section 8). Finally, we note that LP944−020 (Tinney 1996) is no longer a member of the 5 pc sample and 2MASS J1645−1319 is no longer a member of the 10 pc sample (Henry et al. 2006). Table 9 of Dupuy & Liu (2012) lists all known ultra- cool dwarfs with trigonometric parallaxes at the time of that publication. In that list, 156 objects have spectral types matching the spectral type range of our study, M6V to L4. In addition, (b) out of the seventy trigonometric parallaxes reported by Faherty Figure 5. Comparison of photometry for 28 objects observed on both the et al. (2012), 24 are first parallaxes for objects in the M6V to L4 CTIO 0.9 m telescope (Kron–Cousins filters) and the SOI instrument on the spectral type range. The 28 objects for which we publish first SOAR 4.1 m telescope (Bessell filters). The dotted line indicates a 1 to 1 parallaxes in this paper therefore represent a 15.5% increase in relation. The V band is photometrically identical on both systems. Panel “a” the number of objects with trigonometric parallaxes in the M6V shows that there is no systematic difference between RC and RB. Panel “b” to L4 spectral type range, for a total of 208 objects. shows the trend for the I band. The solid line represents the polynomial fit 2 (V − IB ) =−0.0364(V − IC ) +1.4722(V − IC ) − 1.3563. Most of the difference in the I band is likely due to different sensitivities between the two detectors in the far red. The dashed vertical lines indicate the red limit of the 6.3. Effective Temperatures Bessell (1995) color relations for the two filter systems. While the agreement with interferometric measurements shown in Figure 3 makes us confident that our overall methodol- From a mathematical point of view, solving a trigonometric ogy is right, the effective temperatures we derived based on nine parallax consists of fitting the measured apparent displacements bands of photometry are still essentially model-dependent. The of the science target to an ellipse whose eccentricity and uncertainties in temperatures listed in Table 1 and shown by the orientation is predetermined by the target’s position in the error bars in Figure 4 can therefore be interpreted as measures celestial sphere. At the same time, we deconvolve the constant of how accurate the model atmospheres are in a given tempera- linear component of motion due to the object’s . ture range. Inspection of Figure 4 shows that the models work The size of the ellipse’s major and minor axes provide a measure very well for temperatures above 2600 K, with uncertainties of the object’s distance. Figure 6 shows the parallax ellipses for generally smaller than 30 K. The uncertainties then progres- our observations. In these plots, a parallax factor of 1 or −1 sively increase as the temperature lowers and can be greater indicates the target’s maximum apparent displacement from its than 100 K for objects cooler than 2000 K. The turning point mean position in the axis. Because we restricted at 2600 K has been explained by the model authors (Allard the hour angle of our observations to ±30 minutes (Section 4), et al. 2012) as a consequence of solid grain formation starting high parallax factor observations occurred during evening and at that temperature, thus making the atmosphere significantly morning twilight. As is clear from Figure 6, these twilight more complex. observations are essential for determining the parallax ellipse’s The 2012 brought about crucial advances in our ability major axis. The extent to which observations with lower parallax to determine effective temperatures for cool stellar (and sub- factors constrained the final parallax solution depended greatly stellar) atmospheres. First, the publication of the WISE All Sky

11 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

Figure 6. Parallax ellipses for the 37 parallaxes reported in this paper (objects 2 and 3 comprise a wide binary and parallaxes are derived for both components using the same images). The black dots sample the ellipse that each object appears to trace on the sky as a result of Earth’s annual motion. The eccentricity of the ellipse is a function of the target’s location in the celestial sphere, with objects close to the ecliptic plane producing the most eccentric ellipses. Low parallax factor observations provide significant constraints when the ellipse is not markedly eccentric.

Table 5 Targets with Previously Published Parallaxes

ID Name New New Previous Previous Reference πabs (mas) Distance (pc) πabs (mas) Distance (pc) ± +0.36 ± +0.71 1 GJ 1001 BC 77.02 2.07 12.98−0.34 76.86 3.97 13.01−0.63 Henry et al. (2006) − ± +0.04 ± +0.11 11 LP 944 020 155.89 1.03 6.41−0.04 201.40 4.20 4.96−0.10 Tinney (1996) − ± +0.28 ± +0.63 26 2MASS J0847 1532 58.96 0.99 16.96−0.28 76.5 3.5 13.07−0.57 Faherty et al. (2012) ± +0.05 ± +0.11 27 LHS 2065 117.98 0.76 8.47−0.05 117.30 1.50 8.52−0.11 van Altena et al. (1995) ± +0.48 ± +0.41 35 LHS2397Aab 65.83 2.02 15.19−0.45 73.0 2.1 13.78−0.38 Dupuy & Liu (2012) − ± +0.34 ± +0.86 49 DENIS J1539 0520 61.25 1.26 16.32−0.32 64.5 3.4 15.50−0.78 Andrei et al. (2011) − ± +0.10 ± +0.53 54 2MASS J1645 1319 90.12 0.82 11.09−0.10 109.9 6.1 9.01−0.48 Faherty et al. (2012) − ± +0.59 ± +8.08 56 2MASS J1705 0516AB 55.07 1.76 18.15−0.56 45.0 12.0 22.22−4.68 Andrei et al. (2011) ± +1.11 ± a +0.78 62 LHS 4039C 44.38 2.09 22.53−1.01 43.74 1.43 22.86−0.72 Subasavage et al. (2009)

Note. a Weighted mean of A and B components. See Section 8 for details.

Catalog9 provided uniform photometric coverage in the mid- ties to match observational data to fundamental atmospheric pa- infrared for known cool stars and brown dwarfs. Second, as rameters with unprecedented accuracy (Section 5). Despite these already discussed, the publication of the BT-Settl model atmo- recent advances, it is still useful to compare our results with ear- spheres with revised solar metallicities has provided opportuni- lier pioneering work in the field of effective temperature deter- mination for cool atmospheres. Golimowski et al. (2004b) com- 9 http://wise2.ipac.caltech.edu/docs/release/allsky/ puted effective temperatures for 42 M, L, and T, dwarfs based on

12 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

Table 6 Comparison of Effective Temperatures from Different Studies

ID Name Spectral This G2004a G2004a C2008a R2013a Type Work Range (3 Gyr) 30 LHS 292 M6.0V 2588 ± 32 2475–2750 2725 ··· 2700 32 GJ 406 M6.0V 2700 ± 56 2650–2900 2900 ··· ··· 40 LEHPM2−0174 M6.5V 2598 ± 25 ··· ··· ··· 2700 47 LHS 3003 M7.0V 2581 ± 17 2350–2650 2600 ··· ··· 38 LP 851−346 M7.5V 2595 ± 28 ··· ··· ··· 2600 7 LHS 132 M8.0V 2513 ± 29 ··· ··· ··· 2600 27 LHS 2065 M9.0V 2324 ± 27 2150–2425 2400 ··· ··· 58 SIPS J2045−6332 M9.0V 2179 ± 111 ··· ··· ··· 2500 4 BRI B0021−0214 M9.5V 2315 ± 54 2150–2475 2425 ··· ··· 20 2MASS J0746+2000AB L0.0J 2310 ± 51 1900–2225 2200 ··· ··· 44 2MASS J1439+1929 L1.0 2186 ± 100 1950–2275 2250 ··· ··· 41 Kelu-1AB L2.0J 2026 ± 45 2100–2350 2300 ··· ··· 33 DENIS J1058−1548 L3.0 1804 ± 13 1600–1950 1900 ··· ··· 5 2MASS J0036+1821 L3.5 1796 ± 33 1650–1975 1900 1700 ··· 1 GJ 1001 BC L4.5 1725 ± 21 1750–1975 1850 ··· ··· 60 2MASS J2224−0158 L4.5 1567 ± 88 1475–1800 1750 1700 ···

Note. a G2004: Golimowski et al. 2004b; C2008: Cushing et al. 2008; R2013: Rajpurohit et al. 2013. observations in the L (3.4–4.1 μm) and M (4.6–4.8 μm) bands. They first used photometry to calculate bolometric fluxes based on observed spectra, and then used evolutionary models (Bur- rows et al. 1997) to determine a range of effective temperatures based on bolometric luminosities and radii with the assumption of an age range of 0.1 to 10 Gyr as well as a unique value for 3 Gyr. Cushing et al. (2008) determined the effective tempera- tures of nine L and T dwarfs by fitting observed flux-calibrated spectra in the wavelength range 0.6–14.5 μm to their own model atmospheres. Their technique, like ours, has the advantage of relying solely on atmospheric models as opposed to the signifi- cantly more uncertain evolutionary models, as discussed in de- tail in Section 7.2. Finally, Rajpurohit et al. (2013) have recently compared optical spectra (0.52–1.0 μm) for 152 M dwarfs to the same BT-Settl models we use in this study. Twenty-five of their M dwarfs have spectral types of M6V or later. Table 6 compares our results to overlapping objects in these three studies. While it is difficult to generalize from the small overlap amongst the different samples, there is a tendency for our results to be ∼100 K cooler than the others. The cause of this discrepancy is not clear. In the case of Golimowski et al. (2004b), the most likely explanation is that their assumed mean age of 3 Gyr may not be representative of our sample. An Figure 7. HR diagram of Figure 5 with data from Konopacky et al. (2010) age mismatch combined with the significant uncertainty in the over-plotted with open circles. The data agree well at low temperatures, but evolutionary models could easily account for this temperature steadily diverge at higher temperatures. Both data sets have the minimum radius difference. Out of the five objects in common between this at ∼2075 K. study and Rajpurohit et al. (2013), the effective temperature for one object agrees well while three objects have mismatches of the blue end of the SED. Because our method uses twenty of ∼100 K, and another has a significantly larger mismatch. different colors composed of optical, near-infrared, and mid- While we do not know what is causing the different values, we infrared bands, the selective effect of metallicity in optical colors note that the comparison of radii derived with our methodology is ameliorated in our calculations. with empirically measured radii (Section 5, Figure 3) makes In addition to comparisons to other studies with objects in systematic error in our measurements an unlikely explanation. common to ours, we compare the general trends of our HR A temperature difference of ∼100 K would produce a systematic diagram (Figure 4) with the values derived by Konopacky radius difference of 5% to 10% in the temperature range under et al. (2010). That study used Keck AO resolved near infrared consideration, and yet our derived radii have a mean absolute photometry of M and L binaries as well as Hubble Space residual of only 3.4% in a random scatter. Because Rajpurohit Telescope (HST ) resolved optical photometry to derive effective et al. (2013) base their calculations on optical spectra alone, we temperatures and luminosities. Twenty-two of their targets fall in speculate that the discrepancy may be due to the stronger effects the temperature range of our study, but because theirs was a high of metallicity in altering the optical colors of late M dwarfs; a resolution AO study there are no targets in common. Figure 7 small change in metallicity can significantly change the slope shows their results over-plotted on our HR diagram. The large

13 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. uncertainties in Konopacky et al. (2010) make their data difficult to interpret and are probably a result of the lack of mid infrared photometry in their methodology. There is good agreement between their results and ours at cooler temperatures, but the two trends steadily diverge for temperatures above ∼2000 K, with Konopacky et al. (2010) predicting temperatures as much as 500 K cooler for a given luminosity. The discrepancy is probably a result of atmospheric modeling. While the BT-Settl models used in our study predict the rate of atmospheric dust formation and sedimentation for a wide range of temperatures, the “DUSTY” models (Allard et al. 2001) used by Konopacky et al. (2010) assume the extreme case where grains do not settle below the photosphere, thus providing a strong source of opacity. The “DUSTY” models replicate the conditions of L dwarf atmospheres well but gradually become inadequate at hotter temperatures where grain formation is less relevant (Allard et al. 2013). The additional source of opacity then causes the M dwarfs to appear cooler and larger than they really are.

6.4. Color–Magnitude Relations Color–absolute magnitude relations are often the first tools used in estimating the distance to a star or brown dwarf. Deter- mining useful relations using only near infrared colors is chal- (a) lenging for late M and L dwarfs due to the degenerate nature of the near infrared color–magnitude sequence. One possible solu- tion is the use of spectral type–magnitude relations (e.g., Cruz et al. 2003); however, such relations require accurate knowledge of spectral types in a consistent system and are subject to the uncertainties inherent to any discrete classification system. Here we present new color–magnitude relations based on the optical photometry, 2MASS photometry, and trigonometric parallaxes reported in Table 1. Table 7 presents third order polynomial fits for all color–magnitude combinations of the filters VRIJHKs except for those with the color R−I, which becomes degenerate (i.e., nearly vertical) for R − I>2.5. As an example, the first line of Table 7 should be written algebraically as

3 2 MV = 0.21509(V − R) − 2.81698(V − R) +14.16273(V − R) − 1.45226 (±0.53); 1.61  (V − R)  3.64

The relations are an extension of those published in Henry et al. (2004) into the very red optical regime. They are also complementary to the izJ relations of Schmidt et al. (2010). Figure 8 shows the color–absolute magnitude diagrams and polynomial fits for Mv versus (V − Ks ) and MKs versus (R − (b) Ks ). Known binaries as well as objects that are otherwise Figure 8. Example color–absolute magnitude diagrams over-plotted with third elevated in the color–magnitude diagrams were excluded when order polynomial fits. The Mv × (V−K) relation shown in (a) has a particularly computing the polynomial fits. The 1σ uncertainties vary widely low uncertainty (σ = 0.25 mag) due to the steep decrease in V band flux in × − by color and are as small as 0.24 mag for colors that combine the late M and L dwarf sequence. The Mk (R K) relation shown in (b) has a slightly higher uncertainty (σ = 0.28 mag) but is more practical from an the V filter with the JHKs filters. observational point of view due to the difficulty in obtaining V band photometry for L dwarfs. Binary or otherwise elevated objects were excluded from the 6.5. Optical Variability polynomial fits and are shown enclosed with open circles. Panel (b) uses the same labeling scheme as panel (a). Photometric variability in very low-mass stars and brown (A color version of this figure is available in the online journal.) dwarfs has lately become an active area of research because variability can serve as a probe of many aspects of an object’s atmosphere (e.g., Heinze et al. 2013). The leading candidate correspond to the object’s period of rotation. Harding et al. mechanisms thought to cause photometric variability are non- (2011) have suggested that the link between optical variability uniform cloud coverage in L and early T dwarfs (e.g., Radigan and radio variability in two L dwarfs is indicative of auroral et al. 2012; Apai et al. 2013), optical emission due to magnetic emission analogous to that seen in Jupiter. Khandrika et al. +7 activity, and the existence of cooler star spots due to localized (2013) report an overall variability fraction of 36−6% for objects magnetic activity. The period of variability is often thought to with spectral types ranging from L0 to L5 based on their own

14 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

Table 7 Coefficients for Color–Magnitude Polynomial Fits

Abs. Mag. Color Third Order Second Order First Order Constant Range σ

MV V−R 0.21509 −2.81698 14.16273 −1.45226 1.61–3.64 0.53 MV V−I −0.48431 7.02913 −30.24232 55.89960 3.44–6.24 0.64 MV V−J −0.05553 1.34699 −8.78095 32.19850 5.28–9.75 0.30 MV V−H −0.03062 0.79529 −5.04776 23.53283 5.91–11.00 0.24 MV V−K −0.02006 0.54283 −3.22970 19.05263 6.23–11.80 0.25 MV R−J 0.38685 −4.78978 21.67522 −19.02625 3.67–6.19 0.39 MV R−H −0.03466 0.96656 −4.96743 21.51357 4.30–7.44 0.37 MV R−K −0.06296 1.36944 −7.28721 25.94882 5.30–8.24 0.40 MV I−J 1.18205 −9.28970 27.59574 −11.71022 1.84–3.70 0.42 MV I−H 0.24541 −2.81568 13.65365 −4.94381 2.47–4.95 0.48 MV I−K 0.09183 −1.32390 8.75709 −0.69280 2.79–5.75 0.51 MV J−H 5.05439 −19.22739 30.20127 5.70728 0.51–1.25 1.11 MV J−K 4.35996 −22.11834 40.93688 −5.24138 0.80–2.05 0.92 MV H−K 23.11303 −54.44877 51.74136 4.69129 0.29–0.80 0.84 MR V−R 0.21509 −2.81698 13.16273 −1.45226 1.61–3.64 0.53 MR V−I −0.39598 5.59585 −23.46994 44.27366 3.44–6.24 0.60 MR V−J −0.06508 1.48971 −9.70545 32.85954 5.28–9.75 0.33 MR V−H −0.03213 0.78557 −4.94969 21.92657 5.91–11.00 0.28 MR V−K −0.01882 0.47360 −2.65145 16.13934 6.23–11.80 0.27 MR R−J 0.10246 −0.87144 3.43087 7.64284 3.67–6.19 0.31 MR R−H −0.09460 1.86774 −9.85431 28.99232 4.30–7.44 0.26 MR R−K −0.08589 1.71800 −9.39445 28.84437 5.30–8.24 0.28 MR I−J 0.56097 −4.48907 14.76241 −2.05088 1.84–3.70 0.30 MR I−H 0.16178 −1.99780 10.43314 −2.43140 2.47–4.95 0.32 MR I−K 0.05698 −0.92853 6.77139 0.79636 2.79–5.75 0.35 MR J−H 6.18765 −22.77418 31.75342 3.61753 0.51–1.25 0.84 MR J−K 3.81245 −19.70377 36.29580 −4.63378 0.80–2.05 0.69 MR H−K 26.23045 −59.75888 51.53576 3.25785 0.29–0.80 0.65 MI V−R −0.30086 1.51360 1.22679 6.92302 1.61–3.64 0.55 MI V−I −0.48431 7.02913 −31.24230 55.89957 3.44–6.24 0.64 MI V−J −0.08775 2.06323 −14.53807 43.98302 5.28–9.75 0.37 MI V−H −0.05264 1.35632 −10.21586 35.60933 5.91–11.00 0.32 MI V−K −0.03540 0.96451 −7.46468 29.33155 6.23–11.80 0.30 MI R−J 0.05949 −0.06127 −1.61308 15.59044 3.67–6.19 0.37 MI R−H −0.15245 3.02932 −17.57707 43.57051 4.30–7.44 0.29 MI R−K −0.13466 2.76845 −16.87739 44.05227 5.30–8.24 0.29 MI I−J 0.34947 −2.28896 7.32700 3.70661 1.84–3.70 0.26 MI I−H −0.05625 0.65099 −0.12146 8.93958 2.47–4.95 0.27 MI I−K −0.07979 0.96350 −1.79721 11.08030 2.79–5.75 0.30 MI J−H 1.00902 −9.06504 20.09129 4.41802 0.51–1.25 0.76 MI J−K 2.30591 −13.03453 26.79644 −2.67247 0.80–2.05 0.62 MI H−K 6.36493 −24.92761 31.89872 4.41508 0.29–0.80 0.60 MJ V−R −0.33337 2.21935 −2.66206 9.68513 1.61–3.64 0.39 MJ V−I −0.36037 5.32260 −24.29187 45.23880 3.44–6.24 0.45 MJ V−J −0.05553 1.34699 −9.78094 32.19847 5.28–9.75 0.30 MJ V−H −0.03301 0.88633 −6.95483 26.83274 5.91–11.00 0.26 MJ V−K −0.02220 0.63644 −5.19321 22.87309 6.23–11.80 0.25 MJ R−J 0.10247 −0.87144 2.43089 7.64280 3.67–6.19 0.31 MJ R−H −0.07510 1.64461 −10.09617 28.93402 4.30–7.44 0.25 MJ R−K −0.07709 1.67484 −10.64410 31.00300 5.30–8.24 0.26 MJ I−J 0.34947 −2.28897 6.32701 3.70660 1.84–3.70 0.26 MJ I−H −0.01826 0.36899 −0.39111 8.86504 2.47–4.95 0.25 MJ I−K −0.05043 0.71480 −1.94540 10.88528 2.79–5.75 0.26 MJ J−H −1.75450 1.46627 6.33858 6.88885 0.51–1.25 0.52 MJ J−K 0.89335 −5.42563 12.79557 2.55729 0.80–2.05 0.44 MJ H−K −0.71691 −5.04246 13.53644 6.37982 0.29–0.80 0.44 MH V−R −0.14308 0.68377 1.11084 6.14662 1.61–3.64 0.33 MH V−I −0.27640 4.04822 −18.12088 34.99090 3.44–6.24 0.38 MH V−J −0.04698 1.11998 −7.94481 26.92333 5.28–9.75 0.25 MH V−H −0.03062 0.79529 −6.04775 23.53280 5.91–11.00 0.24 MH V−K −0.02177 0.59741 −4.70539 20.62932 6.23–11.80 0.24 MH R−J 0.05414 −0.30135 0.23514 9.78688 3.67–6.19 0.27 MH R−H −0.09460 1.86773 −10.85430 28.99230 4.30–7.44 0.26 MH R−K −0.08348 1.70954 −10.45700 29.39801 5.30–8.24 0.27 MH I−J 0.19024 −1.18253 3.72420 5.16641 1.84–3.70 0.24 MH I−H −0.05625 0.65099 −1.12146 8.93959 2.47–4.95 0.27

15 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

Table 7 (Continued)

Abs. Mag. Color Third Order Second Order First Order Constant Range σ

MH I−K −0.06209 0.76792 −1.96050 10.17762 2.79–5.75 0.28 MH J−H −1.75451 1.46627 5.33858 6.88885 0.51–1.25 0.52 MH J−K 1.03555 −6.09029 13.19045 2.07593 0.80–2.05 0.45 MH H−K 0.29861 −8.11097 14.59934 5.74926 0.29–0.80 0.43 MK V−R −0.00121 −0.37537 3.46600 4.16422 1.61–3.64 0.31 MK V−I −0.20466 3.00271 −13.26362 27.36341 3.44–6.24 0.34 MK V−J −0.03630 0.86706 −6.07434 22.17402 5.28–9.75 0.24 MK V−H −0.02655 0.68316 −5.12699 20.83821 5.91–11.00 0.24 MK V−K −0.02006 0.54283 −4.22970 19.05261 6.23–11.80 0.25 MK R−J 0.04475 −0.23500 0.13773 9.38717 3.67–6.19 0.26 MK R−H −0.10097 1.92794 −11.03651 28.84667 4.30–7.44 0.27 MK R−K −0.08589 1.71800 −10.39445 28.84436 5.30–8.24 0.28 MK I−J 0.14572 −0.88536 2.93380 5.59314 1.84–3.70 0.25 MK I−H −0.09030 0.98749 −2.35957 10.16948 2.47–4.95 0.28 MK I−K −0.07979 0.96350 −2.79722 11.08030 2.79–5.75 0.30 MK J−H −1.86948 1.75166 4.48358 6.92764 0.51–1.25 0.49 MK J−K −1.86948 1.75166 4.48358 6.92764 0.51–1.25 0.49 MK H−K 0.29864 −8.11102 13.59936 5.74925 0.29–0.80 0.43 observations as well as six previous studies (Bailer-Jones & Mundt 2001; Gelino et al. 2002; Koen 2003, 2005; Enoch et al. 2003; Koen et al. 2004). The threshold for variability of these studies ranged from 10 to 36 mmag and were conducted using various photometric bands. We have measured I band photometric variability as part of our parallax observations. Differential photometry of the parallax target is measured with respect to the astrometric reference stars. Any reference star found to be variable to more than 50 mmag is discarded and the remaining stars are used to determine the baseline variability for the field. Details of the procedure are discussed in Jao et al. (2011). Figure 9 shows the 1σ variability for 36 parallax targets.10 Because the parallax targets were mostly fainter than the reference stars, photometric signal-to-noise of the target objects is the limiting factor for sensitivity to variability. This limit becomes more pronounced for cooler and fainter stars, thus creating the upward linear trend for the least variable objects in Figure 9. Because of this trend, we have conservatively set the threshold for deeming a target variable at 15 mmag, as indicated by the dashed line in Figure 9. We detect 13 variable objects out of +9 36, corresponding to an overall variability of 36−7% where the uncertainties are calculated using binomial statistics.11 While Figure 9. I band photometric variability derived from trigonometric parallax observations. The linear increase in minimum variability with decreasing this result is in excellent agreement to that of Khandrika et al. temperature is most likely not real and caused by lower signal-to-noise for fainter +7 (2013)(36−6%), we note that our sample includes spectral types targets. To account for this trend, we established the threshold for deeming a M6V to L4, while theirs ranges from L0 to L5. Targets found target variable at 15 mmag, indicated by the dashed line. Thirteen out of a to be significantly variable are labeled in Figure 9 with their sample of 36 targets are above the threshold and are labeled with the ID number − used in Tables 1 and 4. See Section 8 for a discussion of the three most variable ID numbers. The objects 2MASS J0451 3402 (L0.5, ID 15), targets. 2MASS J1705−0516AB (L0.5 joint type, ID 56), and SIPS J2045−6332 (M9.0V, ID 58) stand out as being much more variable than the rest of the sample. We defer discussion of ± +0.24 84.88 1.71 mas, corresponding to a distance of 11.78−0.23 pc. these objects until Section 8. Figure 10 shows the residuals to the trigonometric parallax solution, denoting the motion of the object’s photocenter once 6.6. DENIS J1454−6604AB: A New Astrometric Binary the parallax reflex motion and the proper motion have been DENIS J1454−6604AB is an L3.5 dwarf first identified by subtracted. The sinusoidal trend in the R.A. axis is a strong Phan-Bao et al. (2008). We report a trigonometric parallax of indication of an unseen companion that is causing the system’s photocenter to move with respect to the reference stars. The absence of a discernible trend in the declination axis indicates 10 GJ 1001BC is photometrically contaminated by the much brighter A component and was therefore excluded from the variability study. that the system must be nearly edge-on and its orbit has an 11 A review of binomial statistics as applied to stellar populations can be orientation that is predominantly east–west. At this stage, it is found in the appendix of Burgasser et al. (2003). not possible to determine the system’s period or component

16 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. (sub)-stellar matter are then ruled by different physics and obey a different equation of state (e.g., Saumon et al. 1995). Once electron degeneracy sets in at the core, the greater gravitational force of a more massive object will cause a larger fraction of the brown dwarf to become degenerate, causing it to have a smaller radius. The mass–radius relation therefore has a pronounced local minimum near the critical mass attained by the most massive brown dwarfs (Chabrier et al. 2009; Burrows et al. 2011). Identifying the stellar/substellar boundary by locating the minimum radius in the stellar/substellar sequence has an advantage over other search methods (e.g., a dynamical mass search): while the values associated with the locus of minimum radius depend on the unconstrained details of evolutionary models (Section 7.2), its existence is a matter of basic physics and is therefore largely model independent. In Figures 11(a) and (b), we re-arrange the HR diagram of Figure 4 to make radius an explicit function of luminos- ity (a) and effective temperature (b). We do not plot the data for LEHPM2−0174 and SIPS J2045−6332, which have abnor- Figure 10. Astrometric residuals indicating a perturbation on the photocenter mally elevated radii and would have made the figures difficult to position for DENIS J1454−6604 with data taken in the I band. The dots read. These two objects are discussed individually in Section 8. correspond to the positions of the system’s photocenter once proper motion and parallax reflex motion are removed. Each solid dot is the nightly average of After excluding the objects marked as known binaries and a typically three consecutive observations. The open dot represents a night with a few other elevated objects that we suspect are binary or young single observation. The lack of a discernible perturbation in the declination axis objects, both diagrams show the inversion of the radius trend indicates that the system is viewed nearly edge-on and that its orbital orientation near the location of the L2.5 dwarf 2MASS J0523−1403. is primarily east–west. Figures 11(a) and (b) can be compared to Figures 3–5 of Burrows et al. (2011) and Figures 1 and 2 of Chabrier et al. masses. While it may appear in Figure 10 that the system has (2009) for insight into how our data fit the predicted local completed nearly half an orbital cycle in the ∼4 yr that we have minimum in the radius trends. While these works examine been monitoring it, unconstrained eccentricity means that the radius as a theoretical function of mass at given isochrones, system may take any amount of time to complete the remainder there is a remarkable similarity between the overall shape of of its orbit. the theoretical mass–radius trend and the luminosity–radius Once the full orbit of a photocentric astrometric system and temperature–radius trends we detect empirically. The real is mapped, determining the mass and luminosity ratio of the data are likely best represented by a combination of isochrones system is a degenerate problem. The same perturbation can that are biased toward the ages at which high-mass substel- be produced by either a system where the companion has a lar objects shine as early L dwarfs (see Section 7.1 and much lower mass and luminosity than the primary or by a Figures 12–15). While Figure 1 of Chabrier et al. (2009)in- system where the components have nearly the same mass and dicates radii as small as ∼0.075 R for the 10 Gyr isochrone, luminosity. We note that a system where the two components we should not expect to see radii this small in this study because are exactly equal would be symmetric about the barycenter substellar objects with that age are no longer in the luminosity and would therefore produce no perturbation at all. The fact range we observed (M6V to L4; Section 2). The same argu- that the system appears elevated in the HR diagram (Figure 4) ment is valid for the figures in Burrows et al. (2011). Indeed, is an indication that the secondary component is contributing because luminosity and temperature are primarily functions of considerable light and that therefore the nearly equal mass mass for stars and primarily functions of mass and age for scenario is more likely. As described in Dieterich et al. (2011), brown dwarfs, our plots in Figure 11 essentially replicate the a single high resolution image where both components are morphology of the mass–radius relation with added dispersion resolved is enough to determine the flux ratio of the components caused by the observed sample’s finite ranges of metallicity and therefore determine individual dynamical masses once the and age. full photocentric orbit has been mapped. 2MASS J0523−1403 has Teff = 2074 ± 27 K, log(L/L) = We will closely monitor this system with the goal of reporting −3.898±0.021, (R/R) = 0.086±0.0031, and V −K = 9.42. the component masses once orbital mapping is complete. While we cannot exclude the possibility of finding a stellar ob- ject with smaller radius, it is unlikely that such an object would 7. DISCUSSION—THE END OF THE be far from the immediate vicinity of 2MASS J0523−1403 STELLAR MAIN SEQUENCE in these diagrams. If cooler and smaller radii stars exist, they One of the most remarkable facts about VLM stars is the should be more abundant than the brown dwarfs forming the fact that a small change in mass or metallicity can bring upward radius trend at temperatures cooler than 1900 K in about profound changes to the basic physics of the object’s Figure 11(b) because such stars would spend the vast major- interior, if the change in mass or metallicity places the object ity of their lives on the main sequence, where their positions in in the realm of the brown dwarfs, on the other side of the the diagrams would be almost constant, whereas brown dwarfs hydrogen burning minimum mass limit. If the object is unable would constantly cool and fade, thus moving to the right in to reach thermodynamic equilibrium through sustained nuclear the plots. We detect no such objects. We note that while the fusion, the object’s collapse will be halted by non-thermal brown dwarfs cooler than 1900 K in Figure 11(b) are brighter electron degeneracy pressure. The macroscopic properties of than any putative lower radius star of the same temperature, the

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(b) Figure 11. (a) Luminosity–radius and (b) temperature–radius diagrams for the observed sample. The targets are the same as in Figure 5 except for LEHPM2−0174 and SIPS J2045−6332, which were excluded for scaling purposes due to their large radii and are discussed in Section 8. These diagrams provide the same fundamental information as an HR diagram, but they make radius easier to visualize. Once known and suspected binaries are excluded, the radius trends have a minimum about 2MASS J0523−1403 (L2.5), indicating the onset of core electron degeneracy for cooler objects. The location and relevance of Kelu-1AB is discussed in Section 8. Versions of these diagrams that use the ID labels in Table 1 and spectral types for plotting symbols are available as supplemental online material. (An extended, color version of this figure is available in the online journal.)

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(b) (b) Figure 12. Evolutionary tracks for the models of (a) Burrows et al. (1997, 1993) Figure 13. Evolutionary tracks for the models of (a) Chabrier et al. (2000)and and (b) Baraffe et al. (1998) over-plotted on the luminosity–radius diagram. (b) Baraffe et al. (2003) over-plotted on the luminosity–radius diagram. Open Dashed lines indicate the continuation of substellar evolutionary tracks where dots represent ages of 0.05, 0.10, 0.12, 0.50, 1.00, and 10.0 Gyr, except for the no data are available. The open circles on the evolutionary tracks represent ages 0.10 M track, which starts at 0.10 Gyr. The circles for older ages are not in the of 0.5, 1.0, 3.0, and 5.0 Gyr from left to right, with the circles for older plotting range in some of the substellar tracks. The circles for older ages overlap ages not in plotting range in some of the substellar tracks. The circles for older each other in the stellar tracks because there is little evolution at those ages. ages overlap each other in the stellar tracks because there is little evolution at The track corresponding to the hydrogen burning minimum mass is plotted with those ages. The track corresponding to the hydrogen burning minimum mass is a dashed line and has its properties summarized in Table 8. The models were plotted with a dashed line and has its properties summarized in Table 8.These computed only at the values where open dots are plotted, with lines connecting diagrams are best seen in color in the online version of the journal. the open dots for visualization purposes only. This diagram is best visualized in color in the online version of the journal. (A color version of this figure is available in the online journal.) (A color version of this figure is available in the online journal.) difference would amount to only ∼0.3 mag, which is not enough to generate a selection effect in our sample definition. sparsely populated because objects in that region must be in a 7.1. A Discontinuity at the End of the Main Sequence very narrow mass and age range. They must be very high mass brown dwarfs that stay in that high luminosity (temperature) Figure 11 shows a relative paucity of objects forming a region for a relatively brief period of time before they fade and gap at temperatures (luminosities) immediately cooler (fainter) cool. The population density increases again to the right of this than 2MASS J0523−1403. This gap is then followed by a gap because that region can be occupied by brown dwarfs with densely populated region where radius has an increasing trend several combinations of age and mass. in both diagrams. Although we cannot at this point exclude the The space density as functions of luminosity and effective hypothesis that this gap is due to statistics of small numbers, temperature inferred from Figure 11 can be compared to we note that the existence of such a gap is consistent with the theoretical mass and luminosity functions, while keeping in onset of the brown dwarf cooling curve. The stellar sequence mind the important caveat that our observed sample is not to the left-hand-side of 2MASS J0523−1403 is well populated volume complete (Section 2). The mass functions of both because VLM stars have extremely long main sequence lives, Burgasser (2004) and Allen et al. (2005) predict a shallow local therefore holding their positions in the diagrams. The space minimum in the space distribution of dwarfs at temperatures immediately to the right-hand-side of 2MASS J0523−1403 is ∼2000 K. In particular, Figure 6 of Burgasser (2004) predicts

19 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

This paper This paper Literature Literature

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(b) (b) Figure 14. Evolutionary tracks for the models of (a) Burrows et al. (1997, 1993) Figure 15. Evolutionary tracks for the models of (a) Chabrier et al. (2000)and and (b) Baraffe et al. (1998) over-plotted on the temperature–radius diagram. (b) Baraffe et al. (2003) over-plotted on the temperature–radius diagram. Open Dashed lines indicate the continuation of substellar evolutionary tracks where dots represent ages of 0.05, 0.10, 0.12, 0.50, 1.00, and 10.0 Gyr, except for the no data are available. The open circles on the evolutionary tracks represent ages 0.10 M track, which starts at 0.10 Gyr. The circles for older ages are not in the of 0.5, 1.0, 3.0, and 5.0 Gyr from left to right, with the circles for older ages plotting range in some of the substellar tracks. The circles for older ages overlap not in the plotting range in some of the substellar tracks. The circles for older each other in the stellar tracks because there is little evolution at those ages. ages overlap each other in the stellar tracks because there is little evolution at The track corresponding to the hydrogen burning minimum mass is plotted with those ages. The track corresponding to the hydrogen burning minimum mass is a dashed line and has its properties summarized in Table 8. The models were plotted with a dashed line and has its properties summarized in Table 8.These computed only at the values where open dots are plotted, with lines connecting diagrams are best seen in color in the online version of the journal. the open dots for visualization purposes only. This diagram is best visualized in (A color version of this figure is available in the online journal.) color in the online version of the journal. (A color version of this figure is available in the online journal.) a relatively sharp drop in space density at 2000 K, in a manner similar to our results. However, the subsequent increase in space in our sample is 2MASS J0523−1403, with Teff = 2074±27 K. density at cooler temperatures is predicted to be gradual in both In summary, one may say that the current mass functions are Burgasser (2004) and Allen et al. (2005) (Figure 2). Neither useful in replicating the overall morphology of our observed mass function predicts the sudden increase in space density we distribution, but do not fully explain the detailed structure we see at ∼1800 K in Figure 11(b). This last point is particularly notice at the end of the stellar main sequence. As we discuss in noteworthy because our sample selection criteria (Section 2) Section 9, only observing a truly volume-complete sample will aims to evenly sample the spectral type sequence. Our selection yield definite answers about population properties such as the effect works against the detection of any variation in space mass function. density as a function of mass and luminosity, and yet we still The discontinuity is even more pronounced in terms of ra- detect a sharper gap between ∼2000 K and ∼1800 K than what dius: whereas radius decreases steadily with decreasing temper- is expected from the mass functions. Burgasser (2004)also ature until the sequence reaches 2MASS J0523−1403 (R = predicts a population with significant stellar content down to 0.086 R), it then not only starts increasing, but it jumps temperatures of ∼1900 K, whereas the temperature–radius and abruptly to a group of objects with R ∼ 0.1 R. The discon- luminosity–radius trends indicate that the coolest stellar object tinuity in radius is also visible as an offset in the HR diagram

20 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al.

Table 8 Properties of Evolutionary Models

Model H. Burning H. Burning H. Burning Metallicitya Min. Stellar Atmospheric Min. Mass (M)Min.Teff (K) Min. log(L/L)(Z/Z) Radius (R/R) Properties Burrows et al. (1993, 1997) 0.0767 1747 −4.21 1.28 0.085 gray with grains Burrows et al. (1993) 0.094 3630 −2.90 0.00 0.090 metal free Baraffe et al. (1998) ∼0.072 1700 −4.26 1.28 0.085 non-gray without grains Chabrier et al. (2000) ∼0.070 1550 −4.42 1.28 0.086 “DUSTY” grains do not settle Baraffe et al. (2003) ∼0.072 1560 −4.47 1.28 0.081 “COND” clear & metal depleted Saumon & Marley (2008) 0.075 1910 −4.00 0.87 0.090 cloudless Saumon & Marley (2008) 0.070 1550 −4.36 0.87 0.092 cloudy, fsed = 2 Our Results ··· ∼2075 ∼−3.9 ··· ∼0.086 ...

Note. a Models with Z/Z = 1.28 and Z/Z = 0.87 were originally meant as solar metallicity models. The new value takes into account the revised solar metallicities of Caffau et al. (2011). (Figure 4). This discontinuity is further evidence of the end of incorporates the state-of-the-art in atmospheric models. The dis- the stellar main sequence and has a simple explanation: whereas crepancy is due in part to the lack of observational constraints stars achieve their minimum radius at the zero age main se- for evolutionary models. While an atmospheric model may be quence, brown dwarfs continue to contract slightly as they cool fully tested against an observed spectrum, testing an evolution- (Burrows et al. 1997; Baraffe et al. 1998, 2003; Chabrier et al. ary model requires accurate knowledge of age and mass. The 2000). Substellar objects with radii falling in the discontinu- available evolutionary models are also hindered by the fact that ity should therefore be high mass late L, T, or Y dwarfs and none of them incorporate the latest revised solar abundances fall outside the luminosity range of our sample (M6V to L4; that are used to translate observed metallicity diagnostic fea- Section 2). We note that this sudden increase in radius is a dif- tures into the number densities for different species used by ferent effect than the previously mentioned sudden decreases the models. The current accepted values for solar abundances in luminosity and temperature, and indeed, it counteracts the (Caffau et al. 2011) constitute a reduction of 22% when com- decrease in luminosity. The fact that these discontinuities occur pared to the original values used by the evolutionary models of at the same location and can be explained by consequences of Burrows et al. 1993, 1997, Baraffe et al. 1998, Chabrier et al. the stellar/substellar boundary provides strong evidence that we 2000, and Baraffe et al. 2003 (e.g., Grevesse et al. 1993), and have indeed detected the boundary. a slight increase of 15% when compared to the Lodders (2003) The above argument for the causes of the discontinuity also values used by Saumon & Marley (2008). We therefore cannot lend credence to the idea that 2MASS J0523−1403 is a star expect any of the models we consider here to be strictly correct, despite the fact that it has the smallest radius in the sample. but comparing their predictions to our results is nevertheless a We note that 2MASS J0523−1403 and the L1.0 dwarf SSSPM useful endeavor. J0829−1309 located immediately to its left fit nicely within Figures 12 through 15 show several evolutionary tracks the linear stellar sequences in Figures 4 and 11. As already from these models over-plotted on our luminosity–radius and discussed, we would also expect stars to be more prevalent temperature–radius diagrams. The evolutionary tracks of the around the locus of minimum radius due to the limited amount clear and cloudy versions of the Saumon & Marley (2008) of time in which a massive brown dwarf would occupy that models have been shown to be in good agreement with the parameter space. Most importantly, there is a difference between models of Baraffe et al. (2003) and Chabrier et al. (2000), the local minimum in the radius trends and the absolute respectively, and are not shown here. Figures 2 and 3 of Saumon minimum. While theory predicts that the object with the smallest &Marley(2008) compare their models to these earlier works. radius should be the most massive brown dwarf (Burrows et al. Table 8 lists the properties predicted for the hydrogen burning 2011), such an object would not attain its minimum radius until it minimum mass tracks for these models. We also include the zero cools down and enters the T and Y dwarf regime and, therefore, metallicity model of Burrows et al. (1993), which is listed to drifts beyond the luminosity range of this study. illustrate the effect of a reduction in metallicity. All models except for the unrealistic zero metallicity model predict the 7.2. Comparison of the HR Diagram to Evolutionary Models hydrogen burning limit at significantly cooler temperatures and lower luminosities than our values. The evolutionary tracks of We now compare our results to the predictions of the Chabrier et al. (2000) and Baraffe et al. (2003) have reasonable most prevalent evolutionary models encompassing the stellar/ agreement with the observations for log(L/L)  −3.5, where substellar boundary (Burrows et al. 1993, 1997; Baraffe et al. objects are solidly in the stellar domain. Chabrier et al. (2000) 1998, 2003; Chabrier et al. 2000, Saumon & Marley 2008).12 has also achieved some success in reproducing the radii of brown All of these models are the combination of an interior structure dwarfs with log(L/L) ∼−4.0 but cannot account for the small model and an atmospheric model used as a boundary condi- radius of 2MASS J0523−1403 and several other stellar objects. tion. As previously discussed, atmospheric models have become And while Burrows et al. (1993, 1997) seems to accurately highly sophisticated and achieved a great degree of success predict the radius of the smallest stars, the model radii are over the last several years. On the other hand, the evolutionary too small everywhere else in the sequence. In sum, we see models we discuss here are older, and none of them currently that at the level of accuracy needed to predict the entirety of our observations these models are for the most part mutually exclusive. 12 We note that while Burrows et al. (1997) is well known for presenting a unified theory of brown dwarf and giant planet evolution, data in that paper While the differences between our results and model predic- concerning the hydrogen burning limit are from Burrows et al. (1993). tions (Table 8) may at first seem large, they must be examined

21 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. of Allen et al. (2005) predicts the mean mass of spectral type L5 to be 0.067 M, and yet comparing our results to evolutionary models shows masses 0.050 M in the L3 temperature range. A discontinuous mass function that produces objects of stellar mass and then jumps to such low masses without producing the intermediate mass objects is not likely. Observations and theory could be reconciled by either increasing the masses associated with the evolutionary tracks or decreasing the radii predicted by our SED fitting technique. We note however that a systemic over-prediction of radius values by our fitting technique would likely manifest itself in a manner independent of spectral type, and would therefore also be noticeable in the stellar part of Figures 12 through 15 and in our comparison to interferometric radii (Figure 3). Finally, we note that while our observations do not address the minimum mass for hydrogen burning, higher values for mass should also be expected as a result of the downward revision Figure 16. Data from Sorahana et al. (2013; open circles) over-plotted on our in solar abundances. Independent confirmation of this effect temperature–radius diagram. Their radius minimum at 1800 K is probably a through a dynamical mass study would further enhance the result of their unrealistically high temperatures for these objects. body of evidence we have presented for the end of the stellar main sequence at values close to those of 2MASS J0523−1402 (L2.5): Teff ∼ 2075 K, log(L/L) ∼−3.9, (R/R) ∼ 0.086, in the context of the recently revised solar abundances (Caffau − = et al. 2011). Lowering the metal content of a (sub)stellar object and V K 9.42. has the effect of decreasing opacities both in the atmosphere 7.3. Comparison of Radii With Other Studies and in the interior. The net effect is a facilitation of radiative transfer from the object’s core to space and thus a decrease in Unfortunately, there are only a few other observational the temperature gradient between the core and the atmosphere. studies that directly measure or calculate radii for objects in Because in the low metallicity scenario energy escapes the stel- the temperature range considered here. These objects are too lar core more easily, maintaining the minimal core temperature faint to be observed by the Kepler mission except as companions necessary for sustained hydrogen burning requires a higher rate to more massive stars. Their faintness also means that they are of energy generation. As shown by the Z/Z = 0 model of likely to remain outside the domain of long baseline optical Table 8, the minimum stellar mass, minimum effective tem- interferometry for the foreseeable future. There are nevertheless perature, and minimum luminosity all increase as a result of a several examples of VLM eclipsing binary companions where decrease in metallicity. The effect of metallicity on the mini- the primary star in the system is an early M dwarf or a solar mum luminosity is particularly strong. When compared to the analogue (e.g., Burrows et al. 2011, and references therein). Burrows Z/Z = 1.28 model, the Z/Z = 0.00 model pro- Such systems are valuable for comparisons regarding mass duces a minimum luminosity that is greater by a factor of 20.4. and radius, but they lack the photometric coverage needed Our results suggest a minimum luminosity that is greater than to calibrate the SED and derive the luminosity in a manner that predicted by the Z/Z = 1.28 models by a factor ranging analogous to this work. We note that the only known eclipsing from ∼2.0 to ∼3.2, depending upon the model chosen. From system where both members are brown dwarfs (Stassun et al. Figure 4 of Burrows et al. (2011), a lower metallicity would also 2006) is a member of the Orion star forming region and is, cause a more pronounced local minimum in the radius trends therefore, only a few million years old. Stassun et al. (2006) we detect in our Figure 11. We note, however, that the Saumon measure radii of 0.669 ± 0.034 R and 0.511 ± 0.026 R for &Marley(2008) models use an abundance that is slightly lower the two components. At such a young age and such large radii, than the currently accepted values, and even though the temper- this system is a valuable probe of early substellar evolution, but ature for the hydrogen burning limit predicted by their cloudless should not be compared to the much older objects we discuss in model is closer to ours, the change in metallicity alone does not this study. completely solve the discrepancy. It is likely that other factors There have been two recent studies that derive the stellar such as the choice of molecular opacity lists and the precise rate parameters needed for placing objects in the HR diagram. As of nuclear reactions also play important roles (M. Marley & D. already mentioned, Konopacky et al. (2010) derived effective Homeier 2013, private communication). temperatures that agree with our values for early L dwarfs It is interesting to note that if we accept the masses of but steadily diverge as the temperature increases (Section 6.3, the several evolutionary tracks shown in Figures 12 through Figure 7), and their errors are ∼200 K. Although their data 15, then three out of the four models (Burrows et al. 1997; are limited at temperatures cooler than ∼2000 K for the Baraffe et al. 1998, 2003) show a jump from stellar masses at determination of a robust radius trend, they also have a local log(L/L) ∼ 3.9(Teff ∼ 2075 K) to masses 0.050 M for minimum in radius at Teff = 2075 K, for 2MASS J2140+16B, cooler objects. The Chabrier et al. (2000) models show a slightly consistent with our results. More recently, Sorahana et al. (2013) smaller jump to masses 0.060 M. This interpretation is derived radii for several L and T dwarfs based on AKARI difficult to reconcile with the idea of a continuous mass function near infrared spectra. They report a sharp radius minimum of for substellar objects. Because more massive objects cool more 0.064 R at 1800 K. Figure 16 shows their results over-plotted in slowly, we would expect to see more brown dwarfs in the mass our temperature–radius plot. There are several reasons why the range of ∼0.070–0.050 M than less massive objects occupying results of Sorahana et al. (2013) deserve further scrutiny. First, it the same temperature range. As an example, the mass function is difficult to imagine the cause of such a sudden drop in radius

22 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. at L dwarf temperatures, and there are questions as to whether or detect is in agreement, if not somewhat higher, to that of Koen not such high densities can be accommodated by any reasonable (2004). It is interesting to note the spike in variability around equation of state (e.g., Saumon et al. 1995). Also, they attempt Teff ∼ 2100 K in Figure 9. Further investigation is needed to to derive the SED based on near infrared spectra alone, covering determine whether this trend has a physical cause associated wavelengths from 1 μmto5μm only. Finally, we note that their with that temperature range or whether this is a coincidence. effective temperatures agree to other studies for most objects but 2MASS J0523−1403 (L2.5 ID 17) is discussed throughout are higher by as much as a few hundred K when compared to this paper as the object closest to the local minimum in the Golimowski et al. (2004b) and Cushing et al. (2008) for objects luminosity–radius and temperature–radius trends (Figure 11). corresponding to the sharp drop in radius. In Section 6.3,we As we discussed in Section 7, there is strong evidence indicating discussed the importance of optical and mid-infrared data when that the end of the stellar main sequence must lie in its proximity deriving effective temperatures. Because Sorahana et al. (2013) in parameter space. The target has been described as having do not use mid-infrared or optical data, their results should be variable radio and Hα emission (Berger 2002; Antonova et al. approached with caution. 2007; Berger et al. 2010). Despite the common association between Hα emission and youth, we note that it is difficult to conceive of a target with such a small radius (R/R = 8. NOTES ON INDIVIDUAL OBJECTS 0.086 ± .0031) as being young. As discussed in Section 6.5, GJ 1001BC (L4.5 ID 1) is a binary L dwarf with nearly equal radio emission is often used as a probe of magnetic fields and luminosity components (Golimowski et al. 2004a). Golimowski may be accompanied by optical variability if they result in et al. (2006, 2007) report a preliminary total system dynamical auroral phenomena. We detect no significant I band variability − ∼ mass of 0.10 M based on orbital mapping using HST and Very for 2MASS J0523 1403 (upper limit 11.7 mmag), meaning Large Telescope. The conservative assumption of a mass ratio that either the star was in a mostly quiescent state during the ∼ − 3:2 based on nearly equal luminosity would make individual 3 yr for which we monitored the target (2010.98 2013.12) masses range between 0.04 M and 0.06 M, thus placing both or that the link between radio emission and I band variability is objects in the brown dwarf regime. We derive T = 1725 ± 21 not universal. eff − and log(L/L) =−4.049±0.48 for each component, assuming SSSPM J0829 1309 (L1.0 ID 23) is an object very similar − the two objects are identical. These numbers are generally above to 2MASS J0523 1403 but slightly more luminous. The two the hydrogen burning limit numbers predicted by models but objects have 1σ uncertainties that overlap in radius and Teff,but below our numbers (Table 8). This inconsistency is further not luminosity. As shown in Figure 11, the location of SSSPM − − evidence that the hydrogen burning limit must happen at higher J0829 1309 is crucial for establishing 2MASS J0523 1403 as luminosities and temperatures than what is predicted by the being close to the minimum of the radius trends. Taken together, − − currently accepted models. 2MASS J0523 1403 and SSSPM J0829 1309 show that the LEHPM1−0494 A (M6.0V ID 3) and B(M9.5VID2)are radius trends in Figure 11 are real, and therefore, the conclusions reported by Caballero (2007) to be a wide common proper we draw in this paper are not the result of one isolated odd object  − motion binary with separation of 78 . We report trigonometric (i.e., 2MASS J0523 1403). 13 parallaxes for both components based on individual reductions LHS 2397aAB (M8.5V (joint) ID 35) is an M8.0V/L7.5 +1.51 binary (Freed et al. 2003). Dupuy et al. (2009) report a total of the same field of view, and derive distances of 26.88−1.36 pc +0.015 +1.40 system dynamical mass of 0.146−0.013 M. Konopacky et al. for the A component and 25.14− pc for the B component 1.26 (2010) derive individual dynamical masses of 0.09 ± 0.06 M for a projected separation of ∼2100 AU. These trigonometric for the primary and 0.06 ± 0.05 M for the secondary. The distances are in good agreement with Caballero’s distance system is therefore an important probe of the hydrogen burning estimate of 23 ± 2 pc and support his claim of a physical mass limit because two coeval components presumably with the association between these two objects. same metallicity lie on opposite sides of the stellar/substellar LHS 1604 (M7.5V ID 12) was first reported by Cruz et al. boundary. We are mapping the astrometric orbit for this system (2007) as being over-luminous by ∼0.6 mag in J. They sug- in a manner similar to that discussed in Section 6.6 for DENIS gested that the near-infrared photometry is consistent with an J1454−6604AB and will publish refined individual dynamical unresolved M7.5V/M9.0V binary. LHS 1604 is the only star in masses as soon as orbital mapping is complete. our sample for which we were not able to calculate T or per- eff LEHPM2−0174 (M6.5V ID 40) appears over-luminous in form an SED fit using the procedures outlined in Section 5—the Figure 4. It is most likely an unresolved multiple, a young fits diverged due to a large infrared excess. We observed LHS object, or both. We note that we could not determine a reliable 1604 using high-resolution laser guide star adaptive optics on source for the spectral type of this object, thus leaving open Gemini North and preliminary results do not show a resolved the possibility that it has been miss-characterized as an M6.5V. companion. We defer a thorough analysis of this target to a LEHPM2−0174 is excluded from Figure 11 because scaling the future publication where we discuss our high-resolution obser- figure to fit its radius (0.173 R) would make the figure difficult vations and use them to place limits on the properties of the to read. putative companion (S. B. Dieterich et al., in preparation). We Kelu-1AB (L2.0 (joint) ID 41) is a well-known L2/L4 bi- are also monitoring LHS 1604 for astrometric perturbations but nary (Liu & Leggett 2005). That study notes that the presence it is too early to notice any trends. of Li λ6708 makes both components substellar with masses 2MASS J0451−3402 (L0.5 ID 15) has the highest photometric 0.06 M according to the lithium test of Rebolo et al. (1992), variability in our sample. It was first noted as a photometrically although they note that the Liλ6708 detection is tenuous. De- variable target by Koen (2004), who reported a sinusoidal trend convolution of this system would provide important informa- with a period of 3.454 days and mean amplitude of ∼1% tion about the hydrogen burning limit due to its location in the (10 mmag), though varying to as high as 4% (40 mmag). While our observations do not have the cadence necessary to obtain phase information, the variability of 51 mmag in the I band we 13 Infrared spectral type for secondary.

23 The Astronomical Journal, 147:94 (25pp), 2014 May Dieterich et al. temperature–radius trend (Figure 11(b)). If we assume that the local minimum in radius signaling the stellar/substellar bound- system is an equal luminosity binary, then the deconvolved radii ary close to the locus of 2MASS J0523−1403 at Teff ∼ 2075 K, of the components are ∼0.089 M. That number would further (R/R) ∼ 0.086, and log(L/L) ∼−3.9. The two panels of constrain the position of 2MASS J0523−1309 as being in the Figure 11 present the evidence for the local minimum in the minimum of the radius trend. However, because the components radius trends as functions of luminosity and temperature. While of Kelu1-AB do not have equal luminosities, we can expect the our sample is not volume complete, it covers the photometric A component to be a more massive brown dwarf or a stellar color range from M6V to L4 in a continuous manner. As we dis- component with mass just above the hydrogen burning limit. cussed in Section 7, our interpretation of the radius trends leaves In either case, the A component would have a smaller radius little chance for the discovery of stellar objects at temperatures than the B component. Determining the precise radius, Teff and cooler than ∼2000 K. luminosity of the A component is crucial for determining the Our plans for the future include making the sample volume- exact location of the point of minimal radius in Figure 11. complete so that population properties such as the mass and 2MASS J1705−0516AB (L0.5 (joint) ID 56) was first reported luminosity functions can be studied with more rigor. We have as an M9V/L3 binary by Reid et al. (2006). The system’s already started a volume-complete astrometric search of all position in the midst of the main sequence in the HR diagram southern systems with primaries having spectral types ranging (Figure 4) shows that the system is dominated by the A from M3V to L5 within 15 pc and would like to extend the component in luminosity. Our parallax observations detect a search to 20 pc and to L7. One of the fundamental questions clear astrometric perturbation. We are working on mapping the that this larger volume-complete search will answer is whether system’s orbit and will soon be able to publish dynamical masses or not the gap we see in Figure 11 after 2MASS J0523−1403 is for the individual components. Like LHS 2397aAB, this system real or whether it is an effect of statistics of small numbers. As will serve as a crucial benchmark system with components likely we discussed in Section 7, the existence of a gap immediately residing on either side of the stellar/substellar boundary. As after the onset of the brown dwarf cooling curve is a natural indicated in Figure 9, this target has one of the largest optical consequence of the fact that only very massive brown dwarfs variabilities in the sample, at 41 mmag in I. We defer a more can occupy that parameter space and do so for a small fraction thorough discussion of 2MASS J1705−0516AB to a future of their lifetimes. As discussed in Section 2, 19 targets are paper (S. B. Dieterich et al., in preparation). still undergoing parallax observations and will be ready for SIPS J2045−6332 (M9.0V ID 58) is an extremely over- placement in the HR diagram during the next few years. These luminous object (Figure 4). We note that unresolved equal targets are mostly L dwarfs. These additional targets constitute luminosity duplicity alone cannot explain the over-luminosity. a powerful test of the ideas we discussed in this work—if The object is also highly variable at 39 mmag in I,asshownin they follow the same trends, they will provide independent Figure 9. The variability suggests that youth may play a role in confirmation of our conclusions. We also plan to perform higher explaining the over-luminosity of SIPS J2045−6332. cadence variability studies on targets with effective temperatures LHS 4039C (M9.0V ID 62) is a member of a triple system 2100 K to investigate the spike in variability we notice for with an M4V primary 102.8 away from LHS 4039C. The third targets just above the hydrogen burning limit (Sections 6.5 and 8, component is a DA white dwarf 6.5 away from the primary Figure 9). (Scholz et al. 2004; Subasavage et al. 2009). Subasavage et al. In this paper, we have addressed the question: “What do (2009) report a trigonometric parallax of 43.74 ± 1.43 mas objects at the stellar/substellar boundary look like to an from the weighted mean of the A and B components. In this observer?” We next plan to populate the HR diagram with paper we have reduced the same data using LHS 4039C as dynamical masses for systems such as GJ 1001BC, LHS the science target and measure a parallax of 44.38 ± 2.09, thus 2397aAB, 2MASS J1705−0516AB (Section 8) as well as the supporting the physical association of the system. The intriguing newly discovered binary DENIS J1454−6604AB (Section 6.6). combination of a white dwarf and a VLM star in the same system Only then we will be able to answer the question: “What are the allows us to constrain the properties of LHS 4039C based on the masses of objects at the stellar/substellar boundary?” Along better understood models of white dwarf evolution. Based on with the answer to the first question, we hope that this work the white dwarf cooling time of 0.81 ± 0.05 Gyr (Subasavage will bring us closer to a complete and thorough understanding et al. 2009) and the progenitor age of 4.4 ± 3.7 Gyr (Iben & of (sub)stellar structure and evolution at the stellar/substellar Laughlin 1989) assuming a progenitor mass of 1.17 ± 0.26 M boundary. (Williams et al. 2009), we infer a total system age of 5.2 ± 3.7 Gyr. Assuming the system to be coeval, LHS4039C is then a This research was supported by NSF grants AST-0507711, main sequence star with no remaining traces of youth. Its locus AST-09-08402, and AST-11-09445. CTIO 0.9 m observa- on the HR diagram is therefore an indication of where the VLM tions were made possible through the SMARTS Consortium. stellar main sequence lies.14 S.B.D. acknowledges travel support for SOAR observing runs from NOAO’s graduate student dissertation support program. 9. CONCLUSIONS AND FUTURE WORK We thank Michael Bessell, Adam Burrows, Adam Burgasser, We have determined fundamental properties (effective tem- Douglas Gies, and Russel White for useful discussions. We also peratures, luminosities, and radii) based on a photometric and thank the anonymous referee for suggestions that increased the astrometric survey of 63 targets with spectral types ranging from quality of the paper. The authors thank the staff of Cerro Tololo M6V to L4, and we used the data to construct an HR diagram of Inter-American Observatory for welcoming us into their coun- the stellar/substellar boundary. We find strong evidence for the try and for their continuous help and support. We are especially grateful to Sean Points, SOAR/SOI Instrument Scientist, for his help and to Steven Heathcote, SOAR Director, for allowing us to 14 It was not possible to label this object in Figure 4 due to crowding of the diagram. The reader is referred to the online supplements where diagrams are stand by on engineering nights and use any remaining time after plotted using ID numbers. engineering activities were concluded. This publication makes

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